bib.bib

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@article {BilleyBergeron,
    AUTHOR = {Bergeron, N. and Billey, S.},
     TITLE = {R{C}-graphs and {S}chubert polynomials},
   JOURNAL = {Experiment. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {2},
      YEAR = {1993},
    NUMBER = {4},
     PAGES = {257--269},
      ISSN = {1058-6458,1944-950X},
   MRCLASS = {05E99 (05E05 14M15 20C30)},
  MRNUMBER = {1281474},
MRREVIEWER = {Axel\ Kohnert},
       URL = {http://projecteuclid.org/euclid.em/1048516036},
}


@article{Defant2024,
author = {Defant, C.},
title = {{Random Subwords and Pipe Dreams}},
journal = {arXiv preprint},
note = {arXiv:2408.05182 [math.PR]},
year = {2024}
}

@unpublished{Lascoux02ice,
    author = {Lascoux, A.},
    title = {{Chern and Yang through ice}},
		note={Unpublished manuscript},
    year = {2002}
}

@article{LamLeeShimozono,
author = {Lam, T. and Lee, S. J. and Shimozono, M.},
doi = {10.1093/imrn/rnac315},
journal = {Int. Math. Res. Not. IMRN},
number = {24},
pages = {21381--21466},
title = {{Back stable $K$-theory Schubert calculus}},
year = {2023},
note={arXiv:2108.10202 [math.CO]}
}


@article{borodin2010adding,
author = {Borodin, A. and Diaconis, P. and Fulman, J.},
journal = {Bull. Amer. Math. Soc.},
note = {arXiv:0904.3740 [math.PR]},
number = {4},
pages = {639--670},
title = {{On adding a list of numbers (and other one-dependent determinantal processes)}},
volume = {47},
year = {2010}
}

@article{tokihiro2005fundamental,
author = {Tokihiro, T. and Mada, J.},
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title = {{Fundamental Cycle of a Periodic Box-Ball System: A Number Theoretical Aspect}},
volume = {47},
year = {2005}
}

@article{tokihiro1996soliton,
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@article{BalagovicKolb2019,
author = {Balagovi\'c, M. and Kolb, S.},
title = {{Universal K-matrix for quantum symmetric pairs}},
journal = {J. Reine Angew. Math.},
year = {2019},
volume = {2019},
number = {747},
pages = {299--353},
doi = {10.1515/crelle-2016-0012}
}

@article{CorwinKnizel2024,
author = {Corwin, I. and Knizel, A.},
title = {{Stationary measure for the open KPZ equation}},
journal = {Comm. Pure Appl. Math.},
year = {2024},
volume = {77},
number = {4},
pages = {2183--2267},
doi = {10.1002/cpa.22174},
note = {arXiv:2103.12253 [math.PR]}
}

@article{corwin2024periodic,
author = {Corwin, I. and Gu, Y. and Sorensen, E.},
journal = {arXiv preprint},
note = {arXiv:2409.03613 [math.PR]},
title = {{Periodic Pitman transforms and jointly invariant measures}},
year = {2023}
}

@article{He2024boundary,
author = {He, J.},
title = {{Boundary current fluctuations for the half-space ASEP and six-vertex model}},
journal = {Proc. London Math. Soc.},
volume = {128},
number = {2},
pages = {e12585},
year = {2024},
note = {arXiv:2303.16335 [math.PR]}
}

@article{slonim2022ballisticity,
author = {Slonim, D. J.},
journal = {Markov Process. Related Fields},
number = {5},
title = {{Ballisticity of Random walks in Random Environments on Z with Bounded Jumps}},
volume = {28},
year = {2022}
}

@article{slonim2024directional,
author = {Slonim, D. J.},
doi = {10.30757/ALEA.v21-27},
journal = {Latin Am. J. Probab. Math. Stat.},
number = {1},
title = {{Directional transience of random walks in random environments with bounded jumps}},
volume = {21},
year = {2024}
}

@article{GrothendieckShenanigans2024,
author = {Morales, A. H. and Panova, G. and Petrov, L. and Yeliussizov, D.},
journal = {arXiv preprint},
note = {arXiv:2407.21653 [math.PR]},
title = {{Grothendieck Shenanigans: Permutons from pipe dreams via integrable probability}},
year = {2024}
}

@article{naruse2019skew,
  author = {Naruse, H. and Okada, S.},
  journal = {Algebraic Combin.},
  number = {4},
  pages = {541--571},
  title = {{Skew hook formula for $d$-complete posets via equivariant $K$-theory}},
  volume = {2},
  year = {2019}
}

@article{konvalinka2020bijective,
  author = {Konvalinka, M.},
  journal = {European J. Combin.},
  pages = {103104},
  title = {{A bijective proof of the hook-length formula for skew shapes}},
  volume = {88},
  year = {2020}
}

@article{felder2023hypergeometric,
  author = {Felder, G. and Smirnov, A. and Tarasov, V. and Varchenko, A.},
  journal = {arXiv preprint},
  note = {arXiv:2308.05766 [math.RT]},
  title = {{Hypergeometric integrals, hook formulas and Whittaker vectors}},
  year = {2023}
}

@article{morales2022asymptotics,
  author = {Morales, A. H. and Pak, I. and Tassy, M.},
  journal = {Combin. Probab. Comput.},
  number = {4},
  pages = {550--573},
  title = {{Asymptotics for the number of standard tableaux of skew shape and weighted lozenge tilings}},
  volume = {31},
  year = {2022}
}

@article{morales2020okounkov,
  author = {Morales, A. H. and Zhu, D. G.},
  journal = {arXiv preprint},
  note = {arXiv:2007.05006 [math.CO]},
  title = {{On the Okounkov-Olshanski formula for standard tableaux of skew shapes}},
  year = {2020}
}

@article{hwang2019reverse,
  author = {Hwang, B.-H. and Kim, J. S. and Yoo, M. and Yun, S.},
  journal = {J. Combin. Theory Ser. A},
  pages = {120--163},
  title = {{Reverse plane partitions of skew staircase shapes and q-Euler numbers}},
  volume = {168},
  year = {2019}
}

@article{morales2023minimal,
  author = {Morales, A. H. and Panova, G. and Park, G.},
  journal = {arXiv preprint},
  note = {arXiv:2311.09209 [math.CO]},
  title = {{Minimal skew semistandard tableaux and the Hillman--Grassl correspondence}},
  year = {2023}
}

@article{park2021naruse,
  author = {Park, G.},
  journal = {arXiv preprint},
  note = {arXiv:2104.11166 [math.CO]},
  title = {{Naruse hook formula for linear extensions of mobile posets}},
  year = {2021}
}

@article{suzuki2021hook,
  author = {Suzuki, T. and Toyosawa, Y.},
  journal = {arXiv preprint},
  note = {arXiv:2106.09254 [math.CO]},
  title = {{On hook formulas for cylindric skew diagrams}},
  year = {2021}
}

@article{kirillov2019hook,
  author = {Kirillov, A. N. and Scrimshaw, T.},
  journal = {arXiv preprint},
  note = {arXiv:1904.00371 [math.CO]},
  title = {{Hook-content formula using excited Young diagrams}},
  year = {2019}
}

@article{morales2018asymptotics,
  author = {Morales, A. H. and Pak, I. and Panova, G.},
  journal = {European J. Combin.},
  pages = {26--49},
  title = {{Asymptotics of the number of standard Young tableaux of skew shape}},
  volume = {70},
  year = {2018}
}

@article{chan2021sorting,
  author = {Chan, S. H. and Pak, I.},
  journal = {Discrete Anal.},
  title = {{Sorting probability for large Young diagrams}},
  year = {2021}
}

@article{kreiman2005schubert,
  author = {Kreiman, V.},
  journal = {arXiv preprint},
  note = {arXiv:math/0512204 [math.AG]},
  title = {{Schubert classes in the equivariant K-theory and equivariant cohomology of the Grassmannian}},
  year = {2005}
}

@inproceedings{mikoda2006number,
author = {Mikoda, A. and Inokuchi, S. and Mizoguchi, Y. and Fujio, M.},
booktitle = {Unconventional Computation},
pages = {181--194},
publisher = {Springer},
series = {Lecture Notes in Computer Science},
title = {{The Number of Orbits of Periodic Box-Ball Systems}},
volume = {4135},
year = {2006}
}

@article {yoshihara-yura-tetsuji-2003,
    AUTHOR = {Yoshihara, D. and Yura, F. and Tokihiro, T.},
     TITLE = {Fundamental cycle of a periodic box-ball system},
   JOURNAL = {J. Phys. A},
  FJOURNAL = {Journal of Physics. A. Mathematical and General},
    VOLUME = {36},
      YEAR = {2003},
    NUMBER = {1},
     PAGES = {99--121},
      ISSN = {0305-4470,1751-8121},
   MRCLASS = {82C20 (68Q80)},
  MRNUMBER = {1958135},
MRREVIEWER = {Min\ Ping\ Qian},
       DOI = {10.1088/0305-4470/36/1/307},
       URL = {https://doi.org/10.1088/0305-4470/36/1/307},
}

@article{petrov2023asymptotics,
author = {Petrov, L. and Tikhonov, M.},
journal = {J. Phys. A: Math. Theor.},
title = {{Asymptotics of noncolliding q-exchangeable random walks}},
year = {2023},
volume = {56},
number = {36},
pages = {365203},
doi = {10.1088/1751-8121/acedda},
note = {arXiv:2303.02380 [math.PR]}
}

@article{kondo2020dynamics,
author = {Kondo, K.},
journal = {arXiv preprint},
note = {arXiv:2003.12974 [math.PR]},
title = {{Dynamics of the multicolor box-ball system with random initial conditions via Pitman's transformation}},
year = {2020}
}

@article{kuniba2020generalized,
author = {Kuniba, A. and Misguich, G. and Pasquier, V.},
journal = {J. Phys. A: Math. Theor.},
note = {arXiv:2004.01569 [math-ph]},
number = {40},
pages = {404001},
title = {{Generalized hydrodynamics in box-ball system}},
volume = {53},
year = {2020}
}

@article{fukuda2004box,
author = {Fukuda, K.},
journal = {J. Algebraic Combin.},
note = {arXiv:math/0105226 [math.CO]},
pages = {67--89},
title = {{Box-Ball Systems and Robinson-Schensted-Knuth Correspondence}},
volume = {19},
year = {2004}
}


@article{ferrari2021soliton,
author = {Ferrari, P. A. and Nguyen, C. and Rolla, L. T. and Wang, M.},
journal = {Forum Math. Sigma},
note = {arXiv:1806.02798 [math-ph]},
pages = {e60},
title = {{Soliton decomposition of the Box-Ball System}},
volume = {9},
year = {2021}
}

@article{croydon2019invariant,
author = {Croydon, D. A. and Sasada, M.},
journal = {J. Math. Phys.},
note = {arXiv:1905.00186 [math.PR]},
pages = {083301},
title = {{Invariant measures for the box-ball system based on stationary Markov chains and periodic Gibbs measures}},
volume = {60},
year = {2019}
}

@article{TakahashiSatsuma1990,
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@article{InoueKunibaTakagi2012,
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@article{crampe2014integrable,
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}

@article{pahuja2023correlations,
author = {Pahuja, N.},
title = {{Correlations in the multispecies PASEP on a ring}},
journal = {arXiv preprint},
year = {2023},
note = {arXiv:2304.13696 [math.CO]}
}

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note = {arXiv:1404.6679 [math.PR]},
pages = {1097--1125},
title = {{Correlations in the multispecies TASEP and a conjecture by Lam}},
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@book{CornfeldFominSinai1982,
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@article{HSY,
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@article{Dodgson1866,
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@book{Lascoux1990,
author = {Lascoux, A.},
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@article{colomo2024scaling,
  author = {Colomo, F. and Pronko, A.G.},
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  note = {arXiv:2407.07849 [math-ph]},
  title = {{Scaling limit of domino tilings on a pentagonal domain}},
  year = {2024}
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@article{borga2020local,
  author = {Borga, J.},
  journal = {Probab. Theory Relat. Fields},
  number = {1},
  pages = {449--531},
  title = {{Local convergence for permutations and local limits for uniform $\rho$-avoiding permutations with $|\rho|= 3$}},
  volume = {176},
  year = {2020},
  note = {arXiv:1807.02702 [math.PR]}
}

@article{BrubakerALCO,
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     title = {Frozen pipes: lattice models for {Grothendieck} polynomials},
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     url = {https://alco.centre-mersenne.org/articles/10.5802/alco.277/}
}


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number = {10},
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title = {{Double Grothendieck Polynomials and Colored Lattice Models}},
volume = {2022},
year = {2022}
}





@article {Proctor90,
    AUTHOR = {Proctor, R.},
     TITLE = {New symmetric plane partition identities from invariant theory
              work of {D}e {C}oncini and {P}rocesi},
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  FJOURNAL = {European Journal of Combinatorics},
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MRREVIEWER = {Tadeusz\ J\'ozefiak},
       DOI = {10.1016/S0195-6698(13)80128-X},
       URL = {https://doi.org/10.1016/S0195-6698(13)80128-X},
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@article {FK,
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       URL = {https://doi.org/10.1023/A:1008694825493},
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  pages = {120--163},
  title = {{Reverse plane partitions of skew staircase shapes and q-Euler numbers}},
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  year = {2019}
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pages = {227--245},
title = {{Determinantal identities for flagged Schur and Schubert polynomials}},
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year = {2016}}

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@book{MacdonaldSchubertBook,
author = {Macdonald, I.G.},
title = {Notes on Schubert Polynomials},
year = {1991},
publisher={Universit\'e du Qu\'ebec \`a Montr\'eal}
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@book{ManivelBook,
author = {Manivel, L.},
title = {{Symmetric functions, Schubert polynomials and degeneracy loci}},
series = {SMF/AMS Texts and Monographs},
volume = {6},
note = {Translated from the 1998 French original by J. R. Swallow},
publisher = {American Mathematical Society, Providence, RI; Soci\'et\'e{} Math\'ematique de France, Paris},
year = {2001},
pages = {viii+167},
isbn = {0-8218-2154-7}
}




@article {MillsRobbinsRumsey,
    AUTHOR = {Mills, W. H. and Robbins, David P. and Rumsey, Jr., Howard},
     TITLE = {Proof of the {M}acdonald conjecture},
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MRREVIEWER = {S.\ Milne},
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       URL = {https://doi.org/10.1007/BF01404757},
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@article{MoralesPakPanova2019,
author = {Morales, A. H. and Pak, I. and Panova, G.},
journal = {Proc. Amer. Math. Soc.},
pages = {1377--1389},
title = {{Asymptotics of principal evaluations of Schubert polynomials for layered permutations}},
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note = {arXiv:1805.04341 [math.CO]}
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@article{colomo2023scaling,
  author = {Colomo, F. and Pronko, A.G.},
  journal = {arXiv preprint},
  note = {arXiv:2407.07849 [math-ph]},
  title = {{Scaling limit of domino tilings on a pentagonal domain}},
  year = {2024}
}

@article{borga2020local,
  author = {Borga, J.},
  journal = {Probab. Theory Relat. Fields},
  number = {1},
  pages = {449--531},
  title = {{Local convergence for permutations and local limits for uniform $\rho$-avoiding permutations with $|\rho|= 3$}},
  volume = {176},
  year = {2020},
  note = {arXiv:1807.02702 [math.PR]}
}

@article{bassino2019universal,
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  number = {11},
  pages = {3565--3639},
  title = {{Universal limits of substitution-closed permutation classes}},
  volume = {22},
  year = {2020}
}

@article {Proctor90,
    AUTHOR = {Proctor, R.},
     TITLE = {New symmetric plane partition identities from invariant theory
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@incollection{TW_Airy_Painleve_2002,
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	publisher = {Amer. Math. Soc., Providence, RI},
	series = {CRM Proc. Lecture Notes},
	title = {Airy kernel and {P}ainlev{\'e} {II}},
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@article{dumitriu2002matrix,
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@book{TaoRMbook,
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@article{Gorin2016,
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	volume = {354},
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@book{Voiculescu_Free_book,
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@article{Novak2012FreeLectures,
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@article{wigner1955characteristic,
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@inproceedings{montgomery1973pair,
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	year = {1973}}

@article{odlyzko1987distribution,
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	volume = {48},
	year = {1987}}

@incollection{keating2006random,
	author = {Keating, J.},
	booktitle = {Applications of random matrices in physics},
	date-added = {2016-01-23 18:19:47 +0000},
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	pages = {1--32},
	publisher = {Springer},
	title = {Random matrices and number theory},
	year = {2006}}

@article{keating2000random,
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	journal = {Commun. Math. Phys.},
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	pages = {57--89},
	publisher = {Springer},
	title = {{Random matrix theory and $\zeta$ (1/2+ it)}},
	volume = {214},
	year = {2000}}

@article{BBP2005phase,
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	journal = {{Ann. Probab.}},
	note = {arXiv:math/0403022 [math.PR]},
	number = {5},
	pages = {1643--1697},
	title = {Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices},
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	year = {2005}}

@article{BorodinEtAl2009TwoSpeed,
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	title = {Two speed TASEP},
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	year = {2009}}

@article{costin2012blockage,
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	note = {arXiv:1207.6555 [math-ph]},
	number = {1},
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	title = {The blockage problem},
	volume = {8},
	year = {2013}}

@article{BaikBBPTASEP,
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	journal = {{Duke Math J.}},
	note = {arXiv:math/0504606 [math.PR]},
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	title = {Painlev\'e formulas of the limiting distributions for nonnull complex sample covariance matrices},
	volume = {133},
	year = {2006}}

@article{wishart1928generalised,
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	date-added = {2016-01-23 17:29:41 +0000},
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	journal = {Biometrika},
	pages = {32-43},
	title = {The generalised product moment distribution in samples from a normal multivariate population},
	volume = {20A},
	year = {1928}}

@article{Hurwitz1897,
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	date-modified = {2023-09-11 12:14:12 -0400},
	journal = {Nachr. Ges. Wiss. G\"ottingen},
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	title = {{\"Uber die Erzeugung der Invarianten durch Integration}},
	year = {1897}}

@article{diaconis2015hurwitz,
	author = {Diaconis, P. and Forrester, P.J.},
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	note = {arXiv:1512.09229 [math-ph]},
	title = {{A. Hurwitz and the origins of random matrix theory in mathematics}},
	year = {2015}}

@article{gotze2010circular,
	author = {G{\"o}tze, F. and Tikhomirov, A.},
	date-added = {2016-01-23 15:09:45 +0000},
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	journal = {{Ann. Probab.}},
	note = {arXiv:0709.3995 [math.PR]},
	number = {4},
	pages = {1444--1491},
	title = {{The circular law for random matrices}},
	volume = {38},
	year = {2010}}

@article{BorodinPetrov2016inhom,
	author = {Borodin, A. and Petrov, L.},
	date-added = {2016-01-17 15:23:09 +0000},
	date-modified = {2018-04-04 23:01:25 +0000},
	journal = {Selecta Math.},
	note = {arXiv:1601.05770 [math.PR]},
	number = {2},
	pages = {751--874},
	title = {Higher spin six vertex model and symmetric rational functions},
	volume = {24},
	year = {2018}}

@article{BorodinBufetov2015,
	author = {Borodin, A. and Bufetov, A.},
	date-added = {2016-01-12 19:12:11 +0000},
	date-modified = {2018-11-13 08:10:54 -0500},
	journal = {Ann. Inst. H. Poincar\'e B},
	note = {arXiv:1509.05070 [math-ph]},
	number = {1},
	pages = {451-463},
	title = {{An irreversible local Markov chain that preserves the six vertex model on a torus}},
	volume = {53},
	year = {2017}}

@article{Wang2015inhomqTASEP,
	author = {Wang, D. and Waugh, D.},
	date-added = {2015-12-08 02:16:57 +0000},
	date-modified = {2015-12-08 02:17:40 +0000},
	journal = {SIGMA. Symmetry, Integrability and Geometry: Methods and Applications},
	note = {arXiv:1512.01612 [math.PR]},
	number = {037},
	title = {{The transition probability of the q-TAZRP (q-Bosons) with inhomogeneous jump rates}},
	volume = {12},
	year = {2016},
	bdsk-url-1 = {http://arxiv.org/abs/1512.01612}}

@article{schutz1997dualityASEP,
	author = {Sch{\"u}tz, G.},
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	date-modified = {2018-02-28 19:41:34 +0000},
	journal = {J. Stat. Phys},
	number = {5-6},
	pages = {1265--1287},
	publisher = {Springer},
	title = {Duality relations for asymmetric exclusion processes},
	volume = {86},
	year = {1997}}

@article{wheeler2015refined,
	author = {Wheeler, M. and Zinn-Justin, P.},
	date-added = {2015-11-03 12:25:04 +0000},
	date-modified = {2015-11-03 12:25:34 +0000},
	journal = {Adv. Math},
	note = {arXiv:1508.02236 [math-ph]},
	pages = {543--600},
	title = {{Refined Cauchy/Littlewood identities and six-vertex model partition functions: III. Deformed bosons}},
	volume = {299},
	year = {2016}}

@article{korff2013cylindric,
	author = {Korff, C.},
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	date-modified = {2015-11-03 12:25:48 +0000},
	journal = {Commun. Math. Phys.},
	note = {arXiv:1110.6356 [math-ph]},
	number = {1},
	pages = {173--246},
	publisher = {Springer},
	title = {{Cylindric versions of specialised Macdonald functions and a deformed Verlinde algebra}},
	volume = {318},
	year = {2013}}

@article{duval2015pieri,
	author = {Duval, A. and Pasquier, V.},
	date-added = {2015-11-03 12:14:31 +0000},
	date-modified = {2015-11-03 12:25:59 +0000},
	note = {arXiv:1510.08709 [math-ph]},
	title = {{Pieri rules, vertex operators and Baxter Q-matrix}},
	year = {2015}}

@article{lam2014rigged,
	author = {Lam, T. and Pylyavskyy, P. and Sakamoto, R.},
	date-added = {2015-10-27 22:45:54 +0000},
	date-modified = {2015-10-27 22:46:29 +0000},
	note = {arXiv:1410.4455 [math.QA]},
	title = {{Rigged configurations and cylindric loop Schur functions}},
	year = {2014}}

@article{tracy2013multi,
	author = {Tracy, C. and Widom, H.},
	date-added = {2015-10-27 22:41:59 +0000},
	date-modified = {2018-02-28 19:41:34 +0000},
	journal = {J. Stat. Phys},
	note = {arXiv:1105.4906 [math.PR]},
	number = {3},
	pages = {457--470},
	publisher = {Springer},
	title = {On the asymmetric simple exclusion process with multiple species},
	volume = {150},
	year = {2013}}

@article{PDF2015qCluster,
	abstract = {In this paper, we construct graded tensor product characters in terms of generalized difference Macdonald raising operators which form a representation of the quantum Q-system. Characters for the graded tensor product of Kirillov-Reshetikhin modules were expressed as the constant term of a non-commutative generating function. This function is written in terms of the generators of a quantum cluster algebra, subject to recursion relations known as the quantum Q-system. The latter form a discrete non-commutative integrable system, with a set of commuting conserved quantities. In type A such conserved quantities can be treated as analogues of the Casimir elements of $U_q({\mathfrak sl}_{r+1})$. We show that the graded tensor product character is the analogue of a class I Whittaker function (to which it reduces in the Demazure case), and that the difference equations which follow from the action of the conserved quantities on characters generalize the difference quantum Toda equations of Etingof. Finally, we construct the graded characters as solutions of these equations, by introducing a representation of the quantum Q-system via difference operators which generalize the Macdonald raising difference operators of Kirillov-Noumi in the dual Whittaker limit.},
	author = {Di Francesco, P. and Kedem, R.},
	date-added = {2015-10-27 16:44:16 +0000},
	date-modified = {2016-08-13 23:41:54 +0000},
	journal = {arXiv preprint},
	note = {arXiv:1505.01657 [math.RT]},
	title = {Difference equations for graded characters from quantum cluster algebra},
	year = {2015}}

@article{rakos2005current,
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	note = {arXiv:cond-mat/0405464 [cond-mat.stat-mech]},
	number = {3-4},
	pages = {511--530},
	publisher = {Springer},
	title = {{Current distribution and random matrix ensembles for an integrable asymmetric fragmentation process}},
	volume = {118},
	year = {2005}}

@article{schutz1997exact,
	author = {Sch{\"u}tz, G.},
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	note = {arXiv:cond-mat/9701019 [cond-mat.stat-mech]},
	number = {1-2},
	pages = {427--445},
	publisher = {Springer},
	title = {Exact solution of the master equation for the asymmetric exclusion process},
	volume = {88},
	year = {1997}}

@article{barraquand2015phase,
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	number = {7},
	pages = {2674--2699},
	title = {{A phase transition for q-TASEP with a few slower particles}},
	volume = {125},
	year = {2015}}

@article{BogoliubovIzerginKitanine98,
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	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=1625167}}

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	title = {{Random-walk in Beta-distributed random environment}},
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	bdsk-url-1 = {http://dx.doi.org/10.1007/s00440-016-0699-z}}

@article{CorwinTsai2015KPZ,
	author = {Corwin, I. and Tsai, L.-C.},
	journal = {arXiv preprint},
	note = {arXiv:1505.04158 [math.PR]},
	title = {{KPZ equation limit of higher-spin exclusion processes}},
	year = {2015}}

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@article{KulishReshSkl1981yang,
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@book{QISM_book,
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	mrclass = {81U40 (81-02 81T40 82-02 82B10)},
	mrreviewer = {Makoto Idzumi},
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	title = {Algebraic {B}ethe ansatz for the elliptic quantum group {$E_{\tau,\eta}({\rm sl}_2)$}},
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	volume = {480},
	year = {1996},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=1421711},
	bdsk-url-2 = {http://dx.doi.org/10.1016/S0550-3213(96)00461-0}}

@incollection{reshetikhin2010lectures,
	author = {Reshetikhin, N.},
	booktitle = {{Exact Methods in Low-dimensional Statistical Physics and Quantum Computing}},
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	date-modified = {2015-08-29 12:05:07 +0000},
	note = {arXiv:1010.5031 [math-ph]},
	pages = {197--266},
	publisher = {Oxford Univ. Press},
	title = {Lectures on the integrability of the 6-vertex model},
	year = {2010}}

@article{KR1987Fusion,
	author = {Kirillov, A.N. and Reshetikhin, N.},
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	journal = {J. Phys. A},
	number = {6},
	pages = {1565--1585},
	title = {{Exact solution of the integrable XXZ Heisenberg model with arbitrary spin. I. The ground state and the excitation spectrum.}},
	volume = {20},
	year = {1987}}

@article{kunibaMangazeev2016stochastic,
	author = {Kuniba, A. and Mangazeev, V. and Maruyama, S. and Okado, M.},
	journal = {Nuclear Physics B},
	note = {arXiv:1604.08304 [math.QA]},
	pages = {248--277},
	title = {{Stochastic $ R $ matrix for $ U_q (A_n^{(1)}) $}},
	url = {https://doi.org/10.1016/j.nuclphysb.2016.09.020},
	volume = {913},
	year = {2016},
	bdsk-url-1 = {https://doi.org/10.1016/j.nuclphysb.2016.09.020}}

@article{Mangazeev2014,
	author = {Mangazeev, V.},
	date-added = {2015-04-15 10:21:12 +0000},
	date-modified = {2015-04-15 10:22:00 +0000},
	journal = {Nuclear Physics B},
	note = {arXiv:1401.6494 [math-ph]},
	pages = {70--96},
	title = {{On the Yang--Baxter equation for the six-vertex model}},
	volume = {882},
	year = {2014}}

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@article{halpin2015kpzCocktail,
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	title = {{A KPZ cocktail-shaken, not stirred...}},
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	year = {2015}}

@article{MikhalkinTropicalAMS,
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@article{dimitrov2020gue,
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	title = {GUE corners process in boundary-weighed six-vertex models},
	year = {2020}}

@article{aggarwal2020nonexistence,
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	journal = {Proc. Lond. Math. Soc.},
	note = {arXiv:2004.13272 [math.PR]},
	title = {{{Nonexistence and uniqueness for pure states of ferroelectric six-vertex models}}},
	year = {2022},
	bdsk-url-1 = {https://doi.org/10.1112/plms.12430}}

@book{Jimbo1994,
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@article{BosnjakMangazeev2016,
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	volume = {359},
	year = {2018}}

@article{jimbo1983solitons,
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@article{KnutsonTao1998JAMS,
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	fjournal = {Journal of the American Mathematical Society},
	issn = {0894-0347},
	journal = {Jour. AMS},
	mrclass = {20G05 (05E05 14M15 52B20)},
	mrreviewer = {Anders Skovsted Buch},
	note = {arXiv:math/9807160 [math.RT]},
	number = {4},
	pages = {1055--1090},
	title = {{The honeycomb model of $GL_n(C)$ tensor products. I. Proof of the saturation conjecture}},
	url = {http://dx.doi.org/10.1090/S0894-0347-99-00299-4},
	volume = {12},
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	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=1671451},
	bdsk-url-2 = {http://dx.doi.org/10.1090/S0894-0347-99-00299-4}}

@article{KnutsonTao2000Notices,
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	fjournal = {Notices of the American Mathematical Society},
	issn = {0002-9920},
	journal = {Notices Amer. Math. Soc.},
	mrclass = {15A18 (20G05)},
	mrreviewer = {Chong Guang Cao},
	note = {arXiv:math/0009048 [math.RT]},
	number = {2},
	pages = {175--186},
	title = {Honeycombs and sums of {H}ermitian matrices},
	volume = {48},
	year = {2001},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=1811121}}

@book{baxter2007exactly,
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	publisher = {Courier Dover Publications},
	title = {{Exactly solved models in statistical mechanics}},
	year = {2007}}

@inproceedings{gelfand1950finite,
	author = {Gelfand, I. and Tsetlin, M.},
	booktitle = {Dokl. Akad. Nauk SSSR},
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@inproceedings{ImamuraSasamotoSpohn2011,
	author = {Imamura, T. and Sasamoto, T. and Spohn, H.},
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	pages = {012016},
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	volume = {297},
	year = {2011}}

@article{BCPS2014,
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	pages = {1167-1245},
	title = {{Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz}},
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@article{CorwinHammond2013,
	author = {Corwin, I. and Hammond, A.},
	date-added = {2014-02-22 00:48:27 +0000},
	date-modified = {2014-02-22 00:48:53 +0000},
	journal = {Probability Theory and Related Fields},
	note = {arXiv:1312.2600 [math.PR]},
	number = {1-2},
	pages = {67--185},
	title = {{KPZ line ensemble}},
	volume = {166},
	year = {2016}}

@article{GorinShkolnikov2014,
	author = {Gorin, V. and Shkolnikov, M.},
	date-added = {2014-02-22 00:36:47 +0000},
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	journal = {Probab. Theory Relat. Fields},
	note = {arXiv:1401.5595 [math.PR]},
	number = {3},
	pages = {413--463},
	title = {{Multilevel Dyson Brownian motions via Jack polynomials}},
	volume = {163},
	year = {2015}}

@article{GorinShkolnikov2012,
	author = {Gorin, V. and Shkolnikov, M.},
	date-added = {2014-02-22 00:32:59 +0000},
	date-modified = {2016-03-31 23:44:53 +0000},
	journal = {Annales de Inst. H. Poincar\'e, Probabilit\'es et Statistiques},
	note = {arXiv:1206.3817 [math.PR]},
	number = {1},
	pages = {18-27},
	title = {{Limits of multilevel TASEP and similar processes}},
	volume = {51},
	year = {2015}}

@article{Corwin2014qmunu,
	author = {Corwin, I.},
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	journal = {Int. Math. Res. Notices},
	note = {arXiv:1401.3321 [math.PR]},
	number = {rnu094},
	title = {{The $q$-Hahn Boson process and $q$-Hahn TASEP}},
	year = {2014}}

@article{Skudlarek1976,
	author = {Skudlarek, H.-L.},
	date-added = {2014-02-07 17:14:44 +0000},
	date-modified = {2014-02-07 17:15:47 +0000},
	journal = {Mathematische Annalen},
	number = {213-231},
	title = {{Die unzerlegbaren Charaktere einiger discreter Gruppen}},
	volume = {223},
	year = {1976}}

@article{KirillovTriangular,
	author = {Kirillov, A.A.},
	date-added = {2014-02-07 16:16:44 +0000},
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	journal = {Trans. AMS},
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	title = {{Variations on the triangular theme}},
	volume = {169},
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@article{BereleRegev,
	author = {Berele, A. and Regev, A.},
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	date-modified = {2014-01-26 22:08:17 +0000},
	journal = {Adv. Math.},
	number = {2},
	pages = {118-175},
	title = {{Hook Young diagrams with applications to combinatorics and representations of Lie superalgebras}},
	volume = {64},
	year = {1987}}

@article{Alvarez1996dualqHahn,
	author = {Alvarez-Nodarse, R. and Smirnov, Y.F.},
	date-added = {2011-08-03 07:49:17 +0000},
	date-modified = {2011-08-03 07:50:33 +0000},
	journal = {Journal of Physics A: Mathematical and General},
	title = {The dual Hahn q-polynomials in the lattice x(s)=[s]q[s+1]q and the q-algebras SUq(2) and SUq(1,1)},
	volume = {29},
	year = {1996}}

@incollection{Klyachko1978,
	author = {Klyachko, A. A.},
	booktitle = {Studies in Number Theory},
	date-added = {2011-06-15 13:43:06 +0400},
	date-modified = {2018-04-14 04:26:11 +0000},
	pages = {59-64},
	publisher = {Izdat. Saratov. Univ.},
	title = {Centralizers of involutions and models of the symmetric and full linear groups},
	volume = {7},
	year = {1978}}

@article{AdlerJohanssonMoerbeke2016tilings,
	author = {Adler, M. and Johansson, K. and van Moerbeke, P.},
	journal = {arXiv preprint},
	note = {arXiv:1609.06995 [math-ph]},
	title = {{Tilings of non-convex polygons, skew-Young tableaux and determinantal processes}},
	year = {2016}}

@electronic{AdlerJvM2011Tacnode,
	author = {Adler, M. and Johansson, K. and van Moerbeke, P.},
	date-added = {2012-10-21 16:41:40 +0000},
	date-modified = {2012-10-21 16:52:41 +0000},
	note = {arXiv:1112.5532 [math.PR]},
	title = {{Double Aztec Diamonds and the Tacnode Process}},
	year = {2011}}

@article{AdlerVM2005VirasoroSchur,
	author = {Adler, M. and van Moerbeke, P.},
	coden = {CPAMA},
	date-added = {2011-11-09 00:11:17 +0000},
	date-modified = {2011-11-09 00:11:31 +0000},
	doi = {10.1002/cpa.20062},
	fjournal = {Communications on Pure and Applied Mathematics},
	issn = {0010-3640},
	journal = {Comm. Pure Appl. Math.},
	mrclass = {60G50 (05E05 05E10 17B68)},
	mrnumber = {2116618 (2005k:60137)},
	mrreviewer = {Steven B. Damelin},
	number = {3},
	pages = {362--408},
	title = {Virasoro action on {S}chur function expansions, skew {Y}oung tableaux, and random walks},
	url = {http://dx.doi.org/10.1002/cpa.20062},
	volume = {58},
	year = {2005},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=2116618},
	bdsk-url-2 = {http://dx.doi.org/10.1002/cpa.20062}}

@electronic{adler-nordenstam2010dyson,
	author = {Adler, M. and Nordenstam, E. and van Moerbeke, P.},
	note = {arXiv:1006.2956 [math.PR]},
	title = {{The Dyson Brownian minor process}},
	year = {2010}}

@article{adler2005virasoro,
	author = {Adler, M. and Van Moerbeke, P.},
	issn = {1097-0312},
	journal = {Communications on Pure and Applied Mathematics},
	note = {arXiv:math/0309202 [math.PR]},
	number = {3},
	pages = {362--408},
	publisher = {Wiley Online Library},
	title = {{Virasoro action on Schur function expansions, skew Young tableaux, and random walks}},
	volume = {58},
	year = {2005}}

@article{AESW51,
	author = {Aissen, M. and Edrei, A. and Schoenberg, I. J. and Whitney, A.},
	date-added = {2011-11-14 16:39:17 +0000},
	date-modified = {2011-11-14 16:39:43 +0000},
	fjournal = {Proceedings of the National Academy of Sciences of the United States of America},
	issn = {0027-8424},
	journal = {Proc. Nat. Acad. Sci. U. S. A.},
	pages = {303--307},
	title = {On the generating functions of totally positive sequences},
	volume = {37},
	year = {1951},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=0041897}}

@article{ASW52,
	author = {Aissen, M. and Schoenberg, I. J. and Whitney, A.},
	date-added = {2012-07-04 14:44:48 +0000},
	date-modified = {2012-07-04 14:45:36 +0000},
	journal = {J. Analyse Math.},
	pages = {93-103},
	title = {{On the generating functions of totally positive sequences I}},
	volume = {2},
	year = {1952}}

@book{Akhiezer1965Moment,
	author = {Akhiezer, N. I.},
	date-added = {2011-11-14 16:18:58 +0000},
	date-modified = {2011-11-14 16:19:51 +0000},
	pages = {x+253},
	publisher = {Hafner Publishing Co., New York},
	series = {Translated by N. Kemmer},
	title = {The classical moment problem and some related questions in analysis},
	year = {1965},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=0184042}}

@article{AlbertsKhaninQuastel2012,
	author = {Alberts, T. and Khanin, K. and Quastel, J.},
	date-added = {2013-10-13 19:42:48 +0000},
	date-modified = {2018-05-28 01:44:41 +0000},
	journal = {{Ann. Probab.}},
	note = {arXiv:1202.4398 [math.PR]},
	number = {3},
	pages = {1212-1256},
	title = {{Intermediate disorder regime for 1+ 1 dimensional directed polymers}},
	volume = {42},
	year = {2014}}

@book{Albeverio2005,
	address = {Providence, RI},
	author = {Albeverio, S. and Gesztesy, F. and H{\o}egh-Krohn, R. and Holden, H.},
	date-added = {2013-10-30 02:12:50 +0000},
	date-modified = {2013-10-30 02:17:00 +0000},
	edition = {second edition},
	publisher = {Amer. Math. Soc.},
	title = {{Solvable models in quantum mechanics}},
	year = {2005}}

@article{Albeverio1998,
	author = {S. Albeverio and Yu. G. Kondratiev and M. Roeckner},
	journal = {Journal of Functional Analysis},
	owner = {leo},
	pages = {444-500},
	timestamp = {2009.08.05},
	title = {{Analysis and Geometry on Configuration Spaces}},
	volume = {154},
	year = {1998}}

@incollection{AldousExchangeability,
	address = {Berlin},
	author = {Aldous, D.},
	booktitle = {{\'Ecole d'\'et\'e de probabilit\'es de Saint-Flour. XIII---1983}},
	date-added = {2012-09-09 19:46:51 +0000},
	date-modified = {2012-09-09 19:49:27 +0000},
	publisher = {Springer-Verlag},
	series = {Lecture Notes in Mathematics},
	title = {Exchangeability and related topics},
	volume = {1117},
	year = {1985},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=883645}}

@article{alimohammadi1999two,
	author = {Alimohammadi, M. and Karimipour, V. and Khorrami, M.},
	date-added = {2013-08-14 02:15:08 +0000},
	date-modified = {2018-02-28 19:41:34 +0000},
	journal = {J. Stat. Phys},
	note = {arXiv:cond-mat/9805155},
	number = {1-2},
	pages = {373-394},
	title = {{A two-parametric family of asymmetric exclusion processes and its exact solution}},
	volume = {97},
	year = {1999}}

@article{AmirCorwinQuastel2011,
	author = {Amir, G. and Corwin, I. and Quastel, J.},
	date-added = {2013-09-05 22:38:07 +0000},
	date-modified = {2016-08-02 02:59:29 +0000},
	journal = {Comm. Pure Appl. Math.},
	note = {arXiv:1003.0443 [math.PR]},
	number = {4},
	pages = {466-537},
	title = {{Probability distribution of the free energy of the continuum directed random polymer in 1+ 1 dimensions}},
	volume = {64},
	year = {2011}}

@article{AmirVirag2011Automaton,
	author = {Amir, G. and Vir{\'a}g, B.},
	date-added = {2011-08-03 07:09:09 +0000},
	date-modified = {2011-08-03 07:09:51 +0000},
	note = {arXiv:1102.4979 [math.PR]},
	title = {Positive speed for high-degree automaton groups}}

@article{BorodinGorinGuionnet2015,
	author = {Borodin, A. and Gorin, V. and Guionnet, A.},
	journal = {Publ. IHES},
	note = {arXiv:1505.03760 [math.PR]},
	pages = {1-78},
	title = {Gaussian asymptotics of discrete $\beta$-ensembles},
	volume = {125},
	year = {2017}}

@article{Johansson_BGG_1998,
	author = {Johansson, K.},
	journal = {Duke Math. J.},
	number = {1},
	pages = {151-204},
	title = {On fluctuations of eigenvalues of random Hermitian matrices},
	volume = {91},
	year = {1998}}

@article{borodin2010clt,
	author = {Borodin, A.},
	note = {arXiv:1011.3544 [math.PR]},
	number = {1},
	publisher = {Mosc. Math. J.},
	title = {{CLT for spectra of submatrices of Wigner random matrices}},
	volume = {14},
	year = {2014}}

@book{AndersonGuionnetZeitouniBook,
	author = {Anderson, G.W. and Guionnet, A. and Zeitouni, O.},
	date-added = {2013-10-26 00:37:52 +0000},
	date-modified = {2013-10-26 00:38:44 +0000},
	publisher = {Cambridge University Press},
	title = {{An introduction to random matrices}},
	year = {2010}}

@book{AndrewsAskeyRoy2000,
	author = {Andrews, G. and Askey, R. and Roy, R.},
	date-added = {2013-10-13 20:17:17 +0000},
	date-modified = {2013-10-13 20:19:41 +0000},
	publisher = {Cambridge University Press},
	title = {{Special Functions}},
	year = {2000}}

@article{Andrews1975,
	author = {George E. Andrews},
	journal = {Proceedings of the American Mathematical Society},
	number = {1},
	owner = {leo},
	pages = {240-245},
	timestamp = {2009.05.29},
	title = {Identities in {C}ombinatorics. {II}: {A} $q$-{A}nalog of the {L}agrange {I}nversion {T}heorem},
	volume = {53},
	year = {1975}}

@article{Antoniak1974,
	author = {Charles E. Antoniak},
	journal = {Ann. Statist.},
	number = {6},
	owner = {leo},
	pages = {1152-1174},
	timestamp = {2010.01.12},
	title = {{Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems}},
	volume = {2},
	year = {1974}}

@article{Aoki2008,
	author = {Aoki, M.},
	journal = {Journal of Economic Dynamics and Control},
	number = {1},
	pages = {66--84},
	publisher = {Elsevier},
	title = {{Thermodynamic limits of macroeconomic or financial models: One-and two-parameter Poisson--Dirichlet models}},
	volume = {32},
	year = {2008}}

@article{Ariki98,
	author = {Ariki, S.},
	date-added = {2013-09-22 15:23:06 +0000},
	date-modified = {2013-09-22 15:25:49 +0000},
	note = {arXiv:math/9910117 [math.QA]},
	title = {{Robinson-Schensted correspondence and left cells}},
	year = {1999}}

@article{Arvesu2006qHahnQuantumG,
	author = {Arvesu, J.},
	date-added = {2011-08-03 07:41:19 +0000},
	date-modified = {2011-08-03 07:42:20 +0000},
	title = {{Quantum algebras SUq(2) and SUq(1,1) associated with certain q-Hahn polynomials: a revisited approach}},
	year = {2006}}

@article{Aval2002,
	abstract = {The aim of this work is to study the quotient ring R_n of the ring
	Q[x_1,...,x_n] over the ideal J_n generated by non-constant homogeneous
	quasi-symmetric functions. We prove here that the dimension of R_n
	is given by C_n, the n-th Catalan number. This is also the dimension
	of the space SH_n of super-covariant polynomials, that is defined
	as the orthogonal complement of J_n with respect to a given scalar
	product. We construct a basis for R_n whose elements are naturally
	indexed by Dyck paths. This allows us to understand the Hilbert series
	of SH_n in terms of number of Dyck paths with a given number of factors.},
	author = {J. -C. Aval and F. Bergeron and N. Bergeron},
	comments = {LaTeX, 3 figures, 12 pages},
	oai2identifier = {math/0202071},
	owner = {leo},
	timestamp = {2009.03.16},
	title = {Ideals of Quasi-Symmetric Functions and Super-Covariant Polynomials for S_n},
	url = {http://arxiv.org/abs/math/0202071},
	year = {2002},
	bdsk-url-1 = {http://arxiv.org/abs/math/0202071}}

@article{Baik1999second,
	author = {Baik, J. and Deift, P. and Johansson, K.},
	date-modified = {2013-08-18 16:40:00 +0000},
	journal = {Geometric And Functional Analysis},
	note = {arXiv:math/9901118 [math.CO]},
	number = {4},
	pages = {702--731},
	publisher = {Springer},
	title = {{On the distribution of the length of the second row of a Young diagram under Plancherel measure}},
	volume = {10},
	year = {2000}}

@article{baik1999distribution,
	author = {Baik, J. and Deift, P. and Johansson, K.},
	date-modified = {2018-02-28 19:36:21 +0000},
	journal = {Jour. AMS},
	note = {arXiv:math/9810105 [math.CO]},
	number = {4},
	pages = {1119--1178},
	publisher = {American Mathematical Society},
	title = {{On the distribution of the length of the longest increasing subsequence of random permutations}},
	volume = {12},
	year = {1999}}

@article{Baik:2011uq,
	abstract = {The notion of r-crossing and r-nesting of a complete match- ing was
	introduced and a symmetry property was proved by Chen, Deng, Du,
	Stanley and Yan in 2007. We consider random matchings of large size
	and study the maximal crossing and the maximal nesting. It is known
	that the marginal distribution of each of them converges to the GOE
	Tracy-Widom distribution. We show that the maximal crossing and the
	maximal nesting becomes independent asymptotically, and eval- uate
	the joint distribution for the Poissonized random matchings explic-
	itly to the first correction term. This leads to an evaluation of
	the asymptotic of the covariance. Furthermore, we compute the explicit
	second correction term of the distributions function of two ob jects:
	(a) the length of the longest increasing subsequence of Poissonized
	random permutation and (b) the maximal crossing, and hence also the
	maximal nesting, of Poissonized random matching.},
	author = {Jinho Baik and Robert Jenkins},
	date-added = {2011-11-03 15:50:53 +0000},
	date-modified = {2011-11-03 15:50:53 +0000},
	title = {Limiting distribution of maximal crossing and nesting of Poissonized random matchings},
	url = {http://arxiv.org/abs/1111.0269v1},
	year = {2011},
	bdsk-url-1 = {http://arxiv.org/abs/1111.0269v1}}

@book{BKMM2003,
	author = {Baik, J. and Kriecherbauer, T. and McLaughlin, K. T.-R. and Miller, P. D.},
	date-added = {2012-02-03 01:19:37 +0000},
	date-modified = {2012-02-03 01:22:17 +0000},
	note = {arXiv:math/0310278 [math.CA]},
	publisher = {Princeton University Press},
	series = {Annals of Mathematics Studies},
	title = {{Discrete Orthogonal Polynomials: Asymptotics and Applications}},
	year = {2007}}

@article{baik_rains2001algebraic,
	author = {Baik, J. and Rains, E.M.},
	date-modified = {2014-10-25 19:09:22 +0000},
	issn = {0012-7094},
	journal = {Duke J. Math.},
	note = {arXiv:math/9905083 [math.CO]},
	number = {1},
	pages = {1--66},
	publisher = {Durham, NC: Duke University Press, 1935-},
	title = {{Algebraic aspects of increasing subsequences}},
	volume = {109},
	year = {2001}}

@article{baik_rains2001asymptotics,
	author = {Baik, J. and Rains, E.M.},
	date-modified = {2014-10-25 19:09:17 +0000},
	issn = {0012-7094},
	journal = {Duke J. Math.},
	note = {arXiv:math/9905084 [math.CO]},
	number = {2},
	pages = {205--282},
	publisher = {Durham, NC: Duke University Press, 1935-},
	title = {{The asymptotics of monotone subsequences of involutions}},
	volume = {109},
	year = {2001}}

@article{baik_rains2001symmetrized,
	author = {Baik, J. and Rains, E.M.},
	journal = {Random matrix models and their applications},
	note = {arXiv:math/9910019 [math.CO]},
	pages = {1--29},
	title = {{Symmetrized random permutations}},
	year = {2001}}

@conference{Bailey2005,
	author = {Sarah Bailey},
	owner = {leo},
	timestamp = {2009.05.02},
	title = {The Symmetric Measure of the Adic Transformation on the Euler Graph},
	year = {2005}}

@conference{Bailey2005a,
	author = {Sarah Bailey and Michael Keane and Karl Petersen and Ibrahim Salama},
	owner = {leo},
	timestamp = {2009.05.02},
	title = {Ergodicity of the Adic Transformation on the Euler Graph},
	year = {2005}}

@article{Balasz_Komjathy_Seppalainen,
	author = {Bal\'asz, M. and Komj\'athy, J. and Sepp{\"a}l{\"a}inen, T.},
	date-added = {2013-08-11 22:17:14 +0000},
	date-modified = {2013-08-11 22:19:11 +0000},
	journal = {Ann. Inst. H. Poincar\'e B},
	pages = {151-187},
	title = {{Microscopic concavity and fluctuation bounds in a class of deposition processes}},
	volume = {48},
	year = {2012}}

@article{Flajolet2002,
	author = {Cyril Banderier and Philippe Flajolet},
	journal = {Theoretical Computer Science},
	owner = {leo},
	pages = {37-80},
	timestamp = {2009.05.30},
	title = {Basic analytic combinatorics of directed lattice paths},
	volume = {281},
	year = {2002}}

@electronic{Bangerezako,
	author = {Bangerezako, G.},
	date-added = {2012-09-17 02:07:31 +0000},
	date-modified = {2012-09-17 02:09:43 +0000},
	note = {Available at \url{http://perso.uclouvain.be/alphonse.magnus/gbang/qbook712.pdf}},
	title = {{An introduction to q-difference equations}},
	url = {http://perso.uclouvain.be/alphonse.magnus/gbang/qbook712.pdf},
	bdsk-url-1 = {http://perso.uclouvain.be/alphonse.magnus/gbang/qbook712.pdf}}

@article{Barbour2000,
	author = {Barbour, AD and Ethier, SN and Griffiths, RC},
	journal = {Annals of Applied Probability},
	pages = {123--162},
	publisher = {Institute of Mathematical Statistics},
	title = {{A transition function expansion for a diffusion model with selection}},
	year = {2000}}

@article{Baryshnikov_GUE2001,
	author = {Baryshnikov, Yu.},
	date-modified = {2018-02-28 19:39:09 +0000},
	journal = {Probab. Theory Relat. Fields},
	owner = {leo},
	pages = {256-274},
	timestamp = {2010.11.19},
	title = {{GUEs and queues}},
	volume = {119},
	year = {2001}}

@article{BatchelorTownsend1949,
	author = {Batchelor, G.K. and Townsend, A.A.},
	date-added = {2013-09-06 00:47:26 +0000},
	date-modified = {2013-09-06 00:51:11 +0000},
	journal = {Proc. R. Soc. London, A},
	number = {1057},
	pages = {238--255},
	title = {The nature of turbulent motion at large wave-numbers},
	volume = {199},
	year = {1949}}

@article{Battle1980,
	author = {Guy A. Battle and Lon Rosen},
	date-modified = {2018-02-28 19:41:34 +0000},
	journal = {J. Stat. Phys},
	number = {2},
	owner = {leo},
	pages = {123-192},
	timestamp = {2009.06.21},
	title = {{The FKG inequality for the Yukawa_2 quantum field theory}},
	volume = {22},
	year = {1980}}

@article{BenkartRoby1998_DownUpAlg,
	abstract = {The algebra generated by the down and up operators on a differential
	partially ordered set (poset) encodes essential enumerative and structural
	properties of the poset. Motivated by the algebras generated by the
	down and up operators on posets, we introduce here a family of infinite-dimensional
	associative algebras called down-up algebras. We show that down-up
	algebras exhibit many of the important features of the universal
	enveloping algebra $U(\fsl)$ of the Lie algebra $\fsl$ including
	a Poincar\'e-Birkhoff-Witt type basis and a well-behaved representation
	theory. We investigate the structure and representations of down-up
	algebras and focus especially on Verma modules, highest weight representations,
	and category $\mathcal O$ modules for them. We calculate the exact
	expressions for all the weights, since that information has proven
	to be particularly useful in determining structural results about
	posets.},
	author = {Benkart, G. and Roby, T.},
	date-added = {2011-09-14 11:16:14 +0000},
	date-modified = {2011-09-14 11:16:45 +0000},
	title = {Down-up Algebras},
	url = {http://arxiv.org/abs/math/9803159v1},
	bdsk-url-1 = {http://arxiv.org/abs/math/9803159v1}}

@article{Berele2009,
	abstract = {In this paper we introduce doubly symmetric functions, arising from
	the equivalence of particular linear combinations of Schur functions
	and hook Schur functions. We study algebraic and combinatorial aspects
	of doubly symmetric functions, in particular as they form a subalgebra
	of the algebra of symmetric functions. This subalgebra is generated
	by the odd power sum symmetric functions. One consequence is that
	a Schur function itself is doubly symmetric if and only if it is
	the Schur function of a staircase shape.},
	author = {Berele, A. and Tenner, B.E.},
	comments = {11 pages},
	date-modified = {2011-12-03 03:16:55 +0000},
	note = {arXiv:0903.5306 [math.CO]},
	oai2identifier = {0903.5306},
	title = {Doubly Symmetric Functions},
	year = {2009},
	bdsk-url-1 = {http://arxiv.org/abs/0903.5306}}

@article{Berestycki2004,
	abstract = {Our work is motivated by Bourque and Pevzner's (2002) simulation study
	of the effectiveness of the parsimony method in studying genome rearrangement,
	and leads to a surprising result about the random transposition walk
	on the group of permutations on $n$ elements. Consider this walk
	in continuous time starting at the identity and let $D_t$ be the
	minimum number of transpositions needed to go back to the identity
	from the location at time $t$. $D_t$ undergoes a phase transition:
	the distance $D_{cn/2} \sim u(c)n$, where $u$ is an explicit function
	satisfying $u(c)=c/2$ for $c \le 1$ and $u(c)1$. In other words,
	the distance to the identity is roughly linear during the subcritical
	phase, and after critical time $n/2$ it becomes sublinear. In addition,
	we describe the fluctuations of $D_{cn/2}$ about its mean in each
	of the threeregimes (subcritical, critical and supercritical). The
	techniques used involve viewing the cycles in the random permutation
	as a coagulation-fragmentation process and relating the behavior
	to the \Erd\H{o}s-Renyi random graph model.},
	author = {Nathanael Berestycki and Rick Durrett},
	comments = {Revisions include considerable changes in the presentation of section 6 (proof of the CLT in the supercritical regime), and several typos corrected. Also, the figures are now available as a separate .ps file},
	oai2identifier = {math/0403259},
	owner = {leo},
	timestamp = {2010.01.12},
	title = {A phase transition in the random transposition random walk},
	year = {2004}}

@article{BergeronLamLi2007TowersAlg,
	abstract = {Bergeron and Li have introduced a set of axioms which guarantee that
	the Grothendieck groups of a tower of algebras $\bigoplus_{n\ge0}A_n$
	can be endowed with the structure of graded dual Hopf algebras. Hivert
	and Nzeutzhap, and independently Lam and Shimozono constructed dual
	graded graphs from primitive elements in Hopf algebras. In this paper
	we apply the composition of these constructions to towers of algebras.
	We show that if a tower $\bigoplus_{n\ge0}A_n$ gives rise to graded
	dual Hopf algebras then we must have $\dim(A_n)=r^nn!$ where $r =
	\dim(A_1)$.},
	author = {Nantel Bergeron and Thomas Lam and Huilan Li},
	date-added = {2011-08-03 15:14:50 +0000},
	date-modified = {2011-08-03 15:15:25 +0000},
	note = {arXiv:0710.3744 [math.CO]},
	title = {Combinatorial Hopf algebras and Towers of Algebras},
	url = {http://arxiv.org/abs/0710.3744v1},
	year = {2007},
	bdsk-url-1 = {http://arxiv.org/abs/0710.3744v1}}

@article{Bergeron2000,
	abstract = {We consider graded representations of the algebra NC of noncommutative
	symmetric functions on the Z-linear span of a graded poset P. The
	matrix coefficients of such a representation give a Hopf morphism
	from a Hopf algebra HP generated by the intervals of P to the Hopf
	algebra of quasi-symmetric functions. This provides a unified construction
	of quasi-symmetric generating functions from different branches of
	algebraic combinatorics, and this construction is useful for transferring
	techniques and ideas between these branches. In particular we show
	that the (Hopf) algebra of Billera and Liu related to Eulerian posets
	is dual to the peak (Hopf) algebra of Stembridge related to enriched
	P-partitions, and connect this to the combinatorics of the Schubert
	calculus for isotropic flag manifolds.},
	author = {Nantel Bergeron and Stefan Mykytiuk and Frank Sottile and Stephanie van Willigenburg},
	comments = {LaTeX 2e, 22 pages Minor corrections, updated references. Complete and final version, to appear in issue of J. Combin. Th. Ser. A dedicated to G.-C. Rota},
	journal = {J. Combin. Th. Ser. A.},
	number = {1/2},
	oai2identifier = {math/0002073},
	owner = {leo},
	pages = {84-110.},
	timestamp = {2009.03.16},
	title = {Non-commutative Pieri operators on posets},
	url = {http://arxiv.org/abs/math/0002073},
	volume = {91},
	year = {2000},
	bdsk-url-1 = {http://arxiv.org/abs/math/0002073}}

@article{Bergeron1999,
	abstract = {In his work on P-partitions, Stembridge defined the algebra of peak
	functions Pi, which is both a subalgebra and a retraction of the
	algebra of quasi-symmetric functions. We show that Pi is closed under
	coproduct, and therefore a Hopf algebra, and describe the kernel
	of the retraction. Billey and Haiman, in their work on Schubert polynomials,
	also defined a new class of quasi-symmetric functions --- shifted
	quasi-symmetric functions --- and we show that Pi is strictly contained
	in the linear span Xi of shifted quasi-symmetric functions. We show
	that Xi is a coalgebra, and compute the rank of the n-th graded component.},
	author = {Nantel Bergeron and Stefan Mykytiuk and Frank Sottile and Stephanie van Willigenburg},
	comments = {9 pages, 4 eps figures, uses epsf.sty. to be presented at FPSAC99 in Barcelona by second author},
	journal = {Discrete Math.},
	oai2identifier = {math/9904105},
	owner = {leo},
	pages = {57-66.},
	reportno = {MSRI 1999-022},
	timestamp = {2009.03.16},
	title = {Shifted Quasi-Symmetric Functions and the Hopf algebra of peak functions},
	url = {http://arxiv.org/abs/math/9904105},
	volume = {256},
	year = {1999},
	bdsk-url-1 = {http://arxiv.org/abs/math/9904105}}

@article{BertiniCancrini1995,
	author = {Bertini, L. and Cancrini, N.},
	date-added = {2013-09-06 23:14:21 +0000},
	date-modified = {2018-02-28 19:41:34 +0000},
	journal = {J. Stat. Phys},
	number = {5-6},
	pages = {1377--1401},
	title = {{The stochastic heat equation: Feynman-Kac formula and intermittence}},
	volume = {78},
	year = {1995}}

@article{SasamotoASEPqj2014,
	author = {Carinci, G. and Giardin{\`a}, C. and Redig, F. and Sasamoto, T.},
	date-modified = {2018-02-28 19:39:09 +0000},
	journal = {Probab. Theory Relat. Fields},
	notes = {arXiv:1407.3367 [math.PR]},
	number = {3},
	pages = {887--933},
	title = {A generalized asymmetric exclusion process with $U_q(\mathfrak{sl}_2)$ stochastic duality},
	volume = {166},
	year = {2016}}

@article{K_Lee_qBoson2013,
	author = {Korhonen, M. and Lee, E.},
	journal = {Jour. Math. Phys.},
	note = {arXiv:1308.4769 [math-ph]},
	pages = {013301},
	title = {The transition probability and the probability for the left-most particle's position of the q-totally asymmetric zero range process},
	volume = {55},
	year = {2014}}

@article{bertiniGiacomin1997stochastic,
	author = {Bertini, L. and Giacomin, G.},
	journal = {Commun. Math. Phys.},
	number = {3},
	pages = {571--607},
	title = {{Stochastic Burgers and KPZ equations from particle systems}},
	volume = {183},
	year = {1997}}

@article{Bertoin2007,
	abstract = {We show that for $0<\alpha<1$ and $\theta>-\alpha$, the Poisson-Dirichlet
	distribution with parameter $(\alpha, \theta)$ is the unique reversible
	distribution of a rather natural fragmentation-coalescence process.
	This completes earlier results in the literature for certain split
	and merge transformations and the parameter $\alpha =0$.},
	author = {Jean Bertoin},
	oai2identifier = {0704.3122},
	owner = {leo},
	timestamp = {2009.06.13},
	title = {Two-parameter Poisson-Dirichlet measures and reversible exchangeable fragmentation-coalescence processes},
	year = {2007}}

@article{betea2011elliptically,
author = {Betea, D.},
journal = {SIGMA},
note = {arXiv:1110.4176 [math-ph]},
pages = {032},
title = {{Elliptically Distributed Lozenge Tilings of a Hexagon}},
volume = {14},
year = {2018}
}

@article{Bethe1931,
	author = {Bethe, H.},
	journal = {Zeitschrift fur Physik},
	owner = {leo},
	pages = {205-226},
	timestamp = {2013.05.29},
	title = {{Zur Theorie der Metalle. I. Eigenwerte und Eigenfunktionen der linearen Atomkette. (On the theory of metals. I. Eigenvalues and eigenfunctions of the linear atom chain)}},
	volume = {71},
	year = {1931}}

@article{biane2001approximate,
	author = {Biane, P.},
	date-added = {2011-09-18 06:22:36 +0000},
	date-modified = {2018-02-28 19:47:21 +0000},
	journal = {Int. Math. Res. Notices},
	note = {arXiv:math/0006111 [math.RT]},
	number = {4},
	pages = {179-192},
	publisher = {Oxford University Press},
	title = {Approximate factorization and concentration for characters of symmetric groups},
	volume = {2001},
	year = {2001}}

@article{BBO2004,
	author = {Biane, P. and Bougerol, P. and O'Connell, N.},
	date-added = {2013-05-10 11:52:49 +0000},
	date-modified = {2014-10-25 19:09:12 +0000},
	journal = {Duke J. Math.},
	note = {arXiv:math/0403171 [math.RT]},
	number = {1},
	pages = {127-167},
	title = {Littelmann paths and brownian paths},
	volume = {130},
	year = {2005}}

@article{BilleyKaiLam1998Vexillary,
	author = {Billey, S. and Kai Lam, T.},
	date-added = {2011-08-03 07:24:17 +0000},
	date-modified = {2011-08-03 07:25:04 +0000},
	journal = {J. Algebr. Comb.},
	number = {2},
	pages = {139--152},
	title = {Vexillary elements in the hyperoctahedral group},
	volume = {8},
	year = {1998}}

@article{Billingsley1972,
	author = {Billingsley, P.},
	journal = {Periodica Mathematica Hungarica},
	number = {1},
	pages = {283--289},
	publisher = {Akad{\'e}miai Kiad{\'o}, co-published with Springer Science+ Business Media BV, Formerly Kluwer Academic Publishers BV},
	title = {{On the distribution of large prime divisors}},
	volume = {2},
	year = {1972}}

@article{Birkner2009,
	author = {Birkner, M. and Blath, J. and Moehle, M. and Steinruecken, M. and Tams, J.},
	journal = {Alea},
	owner = {leo},
	pages = {25-61},
	timestamp = {2009.08.24},
	title = {A modified lookdown construction for the {X}i-{F}leming-{V}iot process with mutation and populations with recurrent bottlenecks},
	volume = {6},
	year = {2009}}

@article{BirmanWenzl1987,
	author = {Birman, J.S. and Wenzl, H.},
	date-added = {2011-06-15 12:40:29 +0400},
	date-modified = {2018-02-28 19:44:38 +0000},
	journal = {Trans. AMS},
	number = {1},
	pages = {249-273},
	title = {Braids, link polynomials and a new algebra},
	volume = {313},
	year = {1989}}

@article{Blackwell1973,
	author = {Blackwell, D. and MacQueen, J.B.},
	journal = {The annals of statistics},
	number = {2},
	pages = {353--355},
	publisher = {Institute of Mathematical Statistics},
	title = {{Ferguson distributions via Polya urn schemes}},
	volume = {1},
	year = {1973}}

@article{blei2010nested,
	author = {Blei, D.M. and Griffiths, T.L. and Jordan, M.I.},
	journal = {Journal of the ACM (JACM)},
	note = {arXiv:0710.0845 [stat.ML]},
	number = {2},
	pages = {1--30},
	publisher = {ACM},
	title = {{The Nested Chinese Restaurant Process and Bayesian Nonparametric Inference of Topic Hierarchies}},
	volume = {57},
	year = {2010}}

@article{Blei2004,
	author = {Blei, D. and Griffiths, T.L. and Jordan, M.I. and Tenenbaum, J.B.},
	journal = {Advances in neural information processing systems},
	pages = {106},
	publisher = {Citeseer},
	title = {{Hierarchical topic models and the nested Chinese restaurant process}},
	volume = {16},
	year = {2004}}

@article{Blei2009,
	author = {Blei, D. and Lafferty, J.},
	journal = {Text Mining: Theory and Applications. Taylor and Francis, London, UK},
	title = {{Topic models}},
	year = {2009}}

@article{Blei2007a,
	author = {Blei, D.M. and Lafferty, J.D.},
	journal = {Annals of Applied Statistics},
	number = {1},
	pages = {17--35},
	title = {{A correlated topic model of science}},
	volume = {1},
	year = {2007}}

@article{Blei2006,
	author = {Blei, D.M. and Lafferty, J.D.},
	booktitle = {Proceedings of the 23rd international conference on Machine learning},
	organization = {ACM},
	pages = {120},
	title = {{Dynamic topic models}},
	year = {2006}}

@article{Blei2003,
	author = {Blei, D.M. and Ng, A.Y. and Jordan, M.I.},
	journal = {Journal of Machine Learning Research},
	pages = {993--1022},
	title = {{Latent Dirichlet Allocation}},
	volume = {3},
	year = {2003}}

@article{Booth1973,
	author = {Booth, TL and Thompson, RA},
	journal = {IEEE Transactions on Computers},
	number = {22},
	pages = {442--450},
	title = {{Applying probability measures to abstract languages}},
	volume = {100},
	year = {1973}}

@incollection{Borodin2009,
	abstract = {We present a list of algebraic, combinatorial, and analytic mechanisms
	that give rise to determinantal point processes.},
	author = {Borodin, A.},
	booktitle = {Oxford Handbook of Random Matrix Theory},
	comments = {This is a contribution to the Oxford Handbook of Random Matrix Theory},
	date-modified = {2016-10-23 14:28:45 +0000},
	editor = {Akemann, G. and Baik, J. and Di Francesco, P.},
	note = {arXiv:0911.1153 [math.PR]},
	publisher = {Oxford University Press},
	title = {Determinantal point processes},
	year = {2011}}

@article{Borodin2010Schur,
	author = {Borodin, A.},
	date-modified = {2012-07-06 09:34:07 +0000},
	journal = {Adv. Math.},
	note = {arXiv:1001.3442 [math.CO]},
	number = {4},
	owner = {leo},
	pages = {2268-2291},
	timestamp = {2010.09.27},
	title = {{Schur dynamics of the Schur processes}},
	volume = {228},
	year = {2011}}

@electronic{Borodin2011lectures,
	author = {Borodin, A.},
	date-added = {2012-11-05 21:54:10 +0000},
	date-modified = {2012-11-05 21:56:05 +0000},
	note = {Lecture notes. Typed by Steven Sam},
	title = {Gibbs measures on branching graphs},
	url = {http://math.berkeley.edu/~svs/borodin/},
	year = {2011},
	bdsk-url-1 = {http://math.berkeley.edu/~svs/borodin/}}

@article{borodin2007periodic,
	author = {Borodin, A.},
	date-modified = {2014-10-25 19:09:09 +0000},
	journal = {Duke J. Math.},
	note = {arXiv:math/0601019 [math.CO]},
	number = {3},
	pages = {391--468},
	title = {{Periodic Schur process and cylindric partitions}},
	volume = {140},
	year = {2007}}

@article{borodin2000harmonic,
	author = {Borodin, A.M.},
	date-added = {2011-09-10 16:27:57 +0000},
	date-modified = {2011-10-17 00:03:12 +0000},
	journal = {Saint-Petersburg Math. J.},
	number = {5},
	pages = {733-759},
	publisher = {Russian Academy of Sciences, Branch of Mathematical Sciences},
	title = {{Harmonic analysis on the infinite symmetric group, and the Whittaker kernel}},
	volume = {12},
	year = {2001}}

@article{borodin2000riemann,
	author = {Borodin, A.},
	date-modified = {2018-02-28 19:47:21 +0000},
	journal = {Int. Math. Res. Notices},
	note = {arXiv:math/9912093 [math.CO]},
	number = {9},
	pages = {467--494},
	publisher = {Hindawi Publishing Corporation, 410 Park Avenue, 15 th Floor,\# 287 pmb, New York, NY, 10022, USA,},
	title = {{Riemann-Hilbert problem and the discrete Bessel Kernel}},
	volume = {2000},
	year = {2000}}

@article{Borodin1995_ext,
	author = {Borodin, A.},
	date-added = {2014-01-19 17:45:54 +0000},
	date-modified = {2014-01-19 17:46:24 +0000},
	journal = {Jour. Math. Sci. (New York)},
	number = {5},
	pages = {3455--3471},
	title = {{The law of large numbers and the central limit theorem for the jordan normal form of large triangular matrices over a finite field}},
	volume = {96},
	year = {1999}}

@article{Borodin1997,
	author = {Borodin, A.},
	journal = {Jour. Math. Sci. (New York)},
	note = {in Russian: Zap. Nauchn. Sem. POMI {\bf{}240\/} (1997), 44--52, 290--291},
	number = {5},
	owner = {leo},
	pages = {3472--3477},
	timestamp = {2009.03.12},
	title = {Multiplicative central measures on the {S}chur graph},
	volume = {96},
	year = {1999}}

@article{borodin1999colored,
	author = {Borodin, A.},
	date-modified = {2018-02-28 19:50:23 +0000},
	journal = {El. Jour. Combin.},
	number = {1},
	pages = {R13},
	title = {{Longest increasing subsequences of random colored permutations}},
	volume = {6},
	year = {1999}}

@article{Borodin1998a,
	abstract = {We study a 2-parametric family of probability measures on the space
	of countable point configurations on the punctured real line (the
	points of the random configuration are concentrated near zero). These
	measures (or, equivalently, point processes) have been introduced
	in Part II (A. Borodin, math.RT/9804087) in connection with the problem
	of harmonic analysis on the infinite symmetric group. The main result
	of the present paper is a determinantal formula for the correlation
	functions. The formula involves a kernel called the matrix Whittaker
	kernel. Each of its two diagonal blocks governs the projection of
	the process on one of the two half-lines; the corresponding kernel
	on the half-line was studied in Part III (A. Borodin and G. Olshanski,
	math/RT/9804088). While the diagonal blocks of the matrix Whitaker
	kernel are symmetric, the whole kernel turns out to be $J$-symmetric,
	i.e., symmetric with respect to a natural indefinite inner product.
	We also discuss a rather surprising connection of our processes with
	the recent work by B. Eynard and M. L. Mehta (cond-mat/9710230) on
	correlations of eigenvalues of coupled random matrices.},
	author = {Borodin, A.},
	comments = {AMSTeX, 17 pages},
	date-modified = {2011-03-24 13:16:33 +0300},
	oai2identifier = {math/9810013},
	owner = {leo},
	timestamp = {2009.11.26},
	title = {{Point Processes and the Infinite Symmetric Group. Part IV: Matrix Whittaker kernel}},
	year = {1998}}

@article{Borodin1998b,
	author = {Borodin, A.},
	doi = {10.1016/S0550-3213(98)00642-7},
	issue = {3},
	journal = {Nuclear Physics B},
	note = {arXiv:math/9804027 [math.CA]},
	pages = {704-732},
	title = {Biorthogonal ensembles},
	volume = {536},
	year = {1998},
	bdsk-url-1 = {https://doi.org/10.1016/S0550-3213(98)00642-7}}

@article{Borodin1995,
	author = {Borodin, A.},
	date-added = {2014-01-19 17:45:09 +0000},
	date-modified = {2014-01-19 17:45:28 +0000},
	journal = {Functional Analysis and Its Applications},
	number = {4},
	pages = {279-281},
	title = {{Limit Jordan normal form of large triangular matrices over a finite field}},
	volume = {29},
	year = {1995}}

@article{BorodinBufetov2013,
	author = {Borodin, A. and Bufetov, A.},
	date-added = {2013-05-15 20:38:30 +0000},
	date-modified = {2016-02-16 02:53:00 +0000},
	journal = {Duke J. Math.},
	note = {arXiv:1301.0511 [math.RT]},
	number = {11},
	pages = {2109-2158},
	title = {{Plancherel representations of $U(\infty)$ and correlated Gaussian Free Fields}},
	volume = {163},
	year = {2014}}

@article{BorodinBufetov2012,
	author = {Borodin, A. and Bufetov, A.},
	date-added = {2013-10-29 19:47:04 +0000},
	date-modified = {2016-02-16 02:52:45 +0000},
	journal = {Zapiski Nauchn. Semin. POMI},
	note = {arXiv:1203.3010 [math.RT]},
	pages = {19-34},
	title = {{A central limit theorem for Plancherel representations of the infinite-dimensional unitary group}},
	volume = {403},
	year = {2012}}

@article{BBO2013,
	author = {Borodin, A. and Bufetov, A. and Olshanski, G.},
	date-added = {2013-10-29 13:28:49 +0000},
	date-modified = {2016-02-16 02:52:57 +0000},
	note = {arXiv:1311.5697 [math.RT]},
	title = {{Limit shapes for growing extreme characters of $U(\infty)$}},
	year = {2013}}

@article{BorodinCorwin2013discrete,
	author = {Borodin, A. and Corwin, I.},
	date-added = {2013-05-20 17:11:57 +0000},
	date-modified = {2018-02-28 19:47:33 +0000},
	journal = {Int. Math. Res. Notices},
	note = {arXiv:1305.2972 [math.PR]},
	number = {2},
	pages = {499-537},
	title = {{Discrete time q-TASEPs}},
	volume = {2015},
	year = {2015},
	bdsk-url-1 = {http://arxiv.org/abs/1305.2972},
	bdsk-url-2 = {http://dx.doi.org/10.1093/imrn/rnt206}}

@article{BorodinCorwin2012Anderson,
	author = {Borodin, A. and Corwin, I.},
	date-added = {2013-09-06 23:12:52 +0000},
	date-modified = {2013-10-13 23:04:53 +0000},
	note = {arXiv:1211.7125 [math.PR], to appear in Ann. Appl. Probab.},
	title = {{On moments of the parabolic Anderson model}},
	year = {2012}}

@article{BorodinCorwin2011Macdonald,
	author = {Borodin, A. and Corwin, I.},
	date-added = {2012-09-17 02:00:24 +0000},
	date-modified = {2018-02-28 19:38:39 +0000},
	journal = {Probab. Theory Relat. Fields},
	note = {arXiv:1111.4408 [math.PR]},
	pages = {225-400},
	title = {Macdonald processes},
	volume = {158},
	year = {2014},
	bdsk-url-1 = {http://arxiv.org/abs/1111.4408}}

@article{BorodinCorwinFerrari2012,
	author = {Borodin, A. and Corwin, I. and Ferrari, P.},
	date-added = {2013-09-07 14:05:25 +0000},
	date-modified = {2016-07-28 20:56:22 +0000},
	journal = {Comm. Pure Appl. Math.},
	note = {arXiv:1204.1024 [math.PR]},
	number = {7},
	pages = {1129--1214},
	title = {{Free energy fluctuations for directed polymers in random media in 1+ 1 dimension}},
	volume = {67},
	year = {2014}}

@article{BorodinCorwinFerrariVeto2013,
	author = {Borodin, A. and Corwin, I. and Ferrari, P. and Veto, B.},
	date-added = {2013-08-05 12:00:20 +0000},
	date-modified = {2016-08-13 12:48:08 +0000},
	journal = {Mathematical Physics, Analysis and Geometry},
	note = {arXiv:1407.6977 [math.PR]},
	number = {1},
	pages = {1-95},
	title = {{Height fluctuations for the stationary KPZ equation}},
	volume = {18},
	year = {2015}}

@article{BCGS2013,
	author = {Borodin, A. and Corwin, I. and Gorin, V. and Shakirov, S.},
	date-added = {2013-05-10 13:46:50 +0000},
	date-modified = {2018-02-28 19:44:38 +0000},
	journal = {Trans. AMS},
	note = {arXiv:1306.0659 [math.PR]},
	number = {3},
	pages = {1517-1558},
	title = {{Observables of Macdonald processes}},
	volume = {368},
	year = {2016}}

@article{BorodinCorwinPetrovSasamoto2013,
	author = {Borodin, A. and Corwin, I. and Petrov, L. and Sasamoto, T.},
	date-added = {2013-08-04 14:20:36 +0000},
	date-modified = {2015-02-12 14:35:09 +0000},
	journal = {Compos. Math.},
	note = {arXiv:1308.3475 [math-ph]},
	number = {1},
	pages = {1-67},
	title = {{Spectral theory for the q-Boson particle system}},
	volume = {151},
	year = {2015}}

@article{BorodinCorwinRemenik,
	author = {Borodin, A. and Corwin, I. and Remenik, D.},
	date-added = {2013-10-26 02:09:47 +0000},
	date-modified = {2015-03-01 12:53:55 +0000},
	journal = {Commun. Math. Phys.},
	note = {arXiv:1206.4573 [math.PR]},
	number = {1},
	pages = {215-232},
	title = {{Log-Gamma polymer free energy fluctuations via a Fredholm determinant identity}},
	volume = {324},
	year = {2013}}

@article{BorodinCorwinSasamoto2012,
	author = {Borodin, A. and Corwin, I. and Sasamoto, T.},
	date-added = {2013-02-06 21:16:35 +0000},
	date-modified = {2015-02-12 14:36:05 +0000},
	journal = {Ann. Probab.},
	note = {arXiv:1207.5035 [math.PR]},
	number = {6},
	pages = {2314-2382},
	title = {{From duality to determinants for q-TASEP and ASEP}},
	volume = {42},
	year = {2014}}

@article{BorFerr08push,
	author = {Borodin, A. and Ferrari, P.},
	date-added = {2012-02-06 14:34:29 +0000},
	date-modified = {2018-02-28 19:50:15 +0000},
	journal = {Electron. J. Probab.},
	note = {arXiv:0707.2813 [math-ph]},
	pages = {1380-1418},
	title = {{Large time asymptotics of growth models on space-like paths I: PushASEP}},
	volume = {13},
	year = {2008}}

@article{BorFerr2008DF,
	abstract = {We construct a family of stochastic growth models in 2+1 dimensions,
	that belong to the anisotropic KPZ class. Appropriate projections
	of these models yield 1+1 dimensional growth models in the KPZ class
	and random tiling models. We show that correlation functions associated
	to our models have determinantal structure, and we study large time
	asymptotics for one of the models. The main asymptotic results are:
	(1) The growing surface has a limit shape that consists of facets
	interpolated by a curved piece. (2) The one-point fluctuations of
	the height function in the curved part are asymptotically normal
	with variance of order ln(t) for time t>>1. (3) There is a map of
	the (2+1)-dimensional space-time to the upper half-plane H such that
	on space-like submanifolds the multi-point fluctuations of the height
	function are asymptotically equal to those of the pullback of the
	Gaussian free (massless) field on H.},
	author = {Borodin, A. and Ferrari, P.},
	date-added = {2013-05-10 12:08:22 +0000},
	date-modified = {2014-10-25 19:13:06 +0000},
	journal = {Commun. Math. Phys.},
	note = {arXiv:0804.3035 [math-ph]},
	pages = {603-684},
	title = {{Anisotropic growth of random surfaces in 2+1 dimensions}},
	volume = {325},
	year = {2014}}

@article{Ferrari2008,
	abstract = {We construct a family of stochastic growth models in 2+1 dimensions,
	that belong to the anisotropic KPZ class. Appropriate projections
	of these models yield 1+1 dimensional growth models in the KPZ class
	and random tiling models. We show that correlation functions associated
	to our models have determinantal structure, and we study large time
	asymptotics for one of the models. The main asymptotic results are:
	(1) The growing surface has a limit shape that consists of facets
	interpolated by a curved piece. (2) The one-point fluctuations of
	the height function in the curved part are asymptotically normal
	with variance of order ln(t) for time t>>1. (3) There is a map of
	the (2+1)-dimensional space-time to the upper half-plane H such that
	on space-like submanifolds the multi-point fluctuations of the height
	function are asymptotically equal to those of the pullback of the
	Gaussian free (massless) field on H.},
	author = {Borodin, A. and Ferrari, P.},
	date-modified = {2013-10-13 23:07:05 +0000},
	note = {arXiv:0804.3035 [math-ph]},
	title = {{Anisotropic growth of random surfaces in 2+1 dimensions}},
	year = {2008}}

@article{BorodinFPS2007,
	author = {Borodin, A. and Ferrari, P. and Pr{\"a}hofer, M. and Sasamoto, T.},
	date-added = {2011-12-05 02:35:11 +0000},
	date-modified = {2012-02-03 21:13:04 +0000},
	journal = {J. Stat. Phys.},
	note = {arXiv:math-ph/0608056},
	number = {5-6},
	pages = {1055-1080},
	title = {Fluctuation properties of the {TASEP} with periodic initial configuration},
	volume = {129},
	year = {2007}}

@article{Borodin2008TASEPII,
	author = {Borodin, A. and Ferrari, P. and Sasamoto, T.},
	date-added = {2012-06-05 08:29:15 +0000},
	date-modified = {2016-08-02 03:01:26 +0000},
	doi = {10.1007/s00220-008-0515-4},
	journal = {Commun. Math. Phys.},
	note = {arXiv:0707.4207 [math-ph]},
	number = {2},
	pages = {417--449},
	title = {{Large Time Asymptotics of Growth Models on Space-like Paths II: PNG and Parallel TASEP}},
	volume = {283},
	year = {2008},
	bdsk-url-1 = {http://www.springerlink.com/content/a104254t32n77821/fulltext.pdf},
	bdsk-url-2 = {http://dx.doi.org/10.1007/s00220-008-0515-4}}

@article{BG2011non,
	author = {Borodin, A. and Gorin, V.},
	date-added = {2013-04-07 13:49:20 +0000},
	date-modified = {2018-02-28 19:39:09 +0000},
	journal = {Probab. Theory Relat. Fields},
	note = {arXiv:1106.1299 [math.PR]},
	number = {3-4},
	pages = {935-997},
	title = {{Markov processes of infinitely many nonintersecting random walks}},
	volume = {155},
	year = {2013}}

@article{BorodinGorin2013beta,
	author = {Borodin, A. and Gorin, V.},
	date-added = {2013-05-15 20:47:10 +0000},
	date-modified = {2016-08-14 16:54:56 +0000},
	journal = {Comm. Pure Appl. Math.},
	note = {arXiv:1305.3627 [math.PR]},
	number = {10},
	pages = {1774-1844},
	title = {{General $\beta$-Jacobi corners process and the Gaussian Free Field}},
	volume = {68},
	year = {2015}}

@incollection{BorodinGorinSPB12,
	author = {Borodin, A. and Gorin, V.},
	booktitle = {{Probability and Statistical Physics in St.\ Petersburg}},
	date-added = {2013-04-09 02:25:37 +0000},
	date-modified = {2016-10-23 14:33:59 +0000},
	note = {arXiv:1212.3351 [math.PR]},
	pages = {155--214},
	publisher = {AMS},
	series = {Proceedings of Symposia in Pure Mathematics},
	title = {Lectures on integrable probability},
	volume = {91},
	year = {2016}}

@article{BorodinGorin2008,
	author = {Borodin, A. and Gorin, V.},
	date-added = {2012-02-03 00:14:20 +0000},
	date-modified = {2012-02-03 00:15:00 +0000},
	journal = {Adv. Math.},
	note = {arXiv:0804.3071 [math.CO]},
	number = {6},
	pages = {1739--1770},
	title = {Shuffling algorithm for boxed plane partitions},
	volume = {220},
	year = {2009}}

@article{borodin-gr2009q,
	author = {Borodin, A. and Gorin, V. and Rains, E.},
	date-modified = {2012-02-03 00:43:41 +0000},
	journal = {Selecta Math.},
	note = {arXiv:0905.0679 [math-ph]},
	number = {4},
	pages = {731--789},
	title = {{q-Distributions on boxed plane partitions}},
	volume = {16},
	year = {2010}}

@article{borodin_kuan_2010_orthogonal,
	author = {Borodin, A. and Kuan, J.},
	date-modified = {2016-08-02 02:59:40 +0000},
	issn = {1097-0312},
	journal = {Comm. Pure Appl. Math.},
	note = {arXiv:0904.2607 [math.RT]},
	number = {7},
	pages = {831--894},
	publisher = {Wiley Online Library},
	title = {{Random surface growth with a wall and Plancherel measures for $O (\infty)$}},
	volume = {63},
	year = {2010}}

@article{BorodinKuan2007U,
	author = {Borodin, A. and Kuan, J.},
	date-added = {2011-11-27 21:58:48 +0000},
	date-modified = {2012-10-09 13:51:41 +0000},
	journal = {Adv. Math.},
	note = {arXiv:0712.1848 [math.RT]},
	number = {3},
	pages = {894--931},
	title = {{Asymptotics of Plancherel measures for the infinite-dimensional unitary group}},
	volume = {219},
	year = {2008},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=2442056}}

@article{Borodin2000b,
	abstract = {We consider the asymptotics of the Plancherel measures on partitions
	of $n$ as $n$ goes to infinity. We prove that the local structure
	of a Plancherel typical partition (which we identify with a Young
	diagram) in the middle of the limit shape converges to a determinantal
	point process with the discrete sine kernel. On the edges of the
	limit shape, we prove that the joint distribution of suitably scaled
	1st, 2nd, and so on rows of a Plancherel typical diagram converges
	to the corresponding distribution for eigenvalues of random Hermitian
	matrices (given by the Airy kernel). This proves a conjecture due
	to Baik, Deift, and Johansson by methods different from the Riemann-Hilbert
	techniques used in their original papers math.CO/9810105 and math.CO/9901118
	and from the combinatorial approach proposed by Okounkov in math.CO/9903176.
	Our approach is based on an exact determinantal formula for the correlation
	functions of the poissonized Plancherel measures involving a new
	kernel on the 1-dimensional lattice. This kernel is expressed in
	terms of Bessel functions and we obtain it as a degeneration of the
	hypergeometric kernel from the paper math.RT/9904010 by Borodin and
	Olshanski. Our asymptotic analysis relies on the classical asymptotic
	formulas for the Bessel functions and depoissonization techniques.},
	author = {Borodin, A. and Okounkov, A. and Olshanski, G.},
	comments = {43 pages, AMS LaTeX, 1 figure, added a section about a commuting difference operator and other material},
	date-modified = {2018-02-28 19:44:20 +0000},
	journal = {Jour. AMS},
	note = {arXiv:math/9905032 [math.CO]},
	number = {3},
	oai2identifier = {math/9905032},
	owner = {leo},
	pages = {481--515},
	timestamp = {2009.11.02},
	title = {{Asymptotics of Plancherel measures for symmetric groups}},
	volume = {13},
	year = {2000}}

@incollection{borodin2006stochastic,
	author = {Borodin, A. and Olshanski, G.},
	booktitle = {Representation Theory, Dynamical Systems, and Asymptotic Combinatorics},
	editor = {V. Kaimanovich and A. Lodkin},
	journal = {Representation theory, dynamical systems, and asymptotic combinatorics},
	pages = {9--22, arXiv:math-ph/0402064},
	publisher = {Transl. AMS},
	series = {2},
	title = {{Stochastic dynamics related to Plancherel measure on partitions}},
	volume = {217},
	year = {2006}}

@incollection{Borodin1999RSK,
	abstract = {We suggest an hierarchy of all the results known so far about the
	connection of the asymptotics of combinatorial or representation
	theoretic problems with ``beta=2 ensembles'' arising in the random
	matrix theory. We show that all such results are, essentially, degenerations
	of one general situation arising from so-called generalized regular
	representations of the infinite symmetric group.},
	address = {Cambridge},
	author = {Borodin, A. and Olshanski, G.},
	booktitle = {Random matrix models and their applications},
	date-added = {2011-09-12 03:18:40 +0000},
	date-modified = {2011-12-03 03:20:09 +0000},
	editor = {P.M.Bleher and R.A.Its},
	note = {arXiv:math/9905189 [math.CO]},
	pages = {71-94},
	publisher = {Cambridge Univ. Press},
	series = {Math. Sci. Res. Inst. Publ},
	title = {{Z-Measures on partitions, Robinson-Schensted-Knuth correspondence, and $\beta=2$ random matrix ensembles}},
	volume = {40},
	year = {2001},
	bdsk-url-1 = {http://arxiv.org/abs/math/9905189v1}}

@article{BorodinOlsh2011Bouquet,
	author = {Borodin, A. and Olshanski, G.},
	date-added = {2011-11-13 02:46:41 +0000},
	date-modified = {2013-10-27 16:30:49 +0000},
	journal = {Moscow Mathematical Journal},
	note = {arXiv:1110.4458 [math.RT]},
	number = {2},
	pages = {193-232},
	title = {{The Young bouquet and its boundary}},
	volume = {13},
	year = {2013}}

@article{BorodinOlsh2011GT,
	abstract = {The Gelfand-Tsetlin graph is an infinite graded graph that encodes
	branching of irreducible characters of the unitary groups. The boundary
	of the Gelfand-Tsetlin graph has at least three incarnations ---
	as a discrete potential theory boundary, as the set of finite indecomposable
	characters of the infinite-dimensional unitary group, and as the
	set of doubly infinite totally positive sequences. An old deep result
	due to Albert Edrei and Dan Voiculescu provides an explicit description
	of the boundary; it can be realized as a region in an infinite-dimensional
	coordinate space.},
	author = {Borodin, A. and Olshanski, G.},
	date-added = {2011-11-20 22:34:13 +0000},
	date-modified = {2012-08-16 18:16:35 +0000},
	journal = {Adv. Math.},
	note = {arXiv:1109.1412 [math.CO]},
	pages = {1738--1779},
	title = {{The boundary of the Gelfand-Tsetlin graph: A new approach}},
	volume = {230},
	year = {2012},
	bdsk-url-1 = {http://arxiv.org/abs/1109.1412v1}}

@article{BorodinOlshanski2010GTs,
	abstract = {We construct a four-parameter family of Markov processes on infinite
	Gelfand-Tsetlin schemes that preserve the class of central (Gibbs)
	measures. Any process in the family induces a Feller Markov process
	on the infinite-dimensional boundary of the Gelfand-Tsetlin graph
	or, equivalently, the space of extreme characters of the infinite-dimensional
	unitary group U(infinity). The process has a unique invariant distribution
	which arises as the decomposing measure in a natural problem of harmonic
	analysis on U(infinity) posed in arXiv:math/0109193. As was shown
	in arXiv:math/0109194, this measure can also be described as a determinantal
	point process with a correlation kernel expressed through the Gauss
	hypergeometric function.},
	author = {Borodin, A. and Olshanski, G.},
	date-modified = {2013-01-16 20:21:16 +0000},
	journal = {Journal of Functional Analysis},
	note = {arXiv:1009.2029 [math.PR]},
	number = {1},
	oai2identifier = {1009.2029},
	owner = {leo},
	pages = {248-303},
	timestamp = {2010.10.11},
	title = {{Markov processes on the path space of the Gelfand-Tsetlin graph and on its boundary}},
	volume = {263},
	year = {2012}}

@article{Borodin2007,
	abstract = {The present paper originated from our previous study of the problem
	of harmonic analysis on the infinite symmetric group. This problem
	leads to a family {P_z} of probability measures, the z-measures,
	which depend on the complex parameter z. The z-measures live on the
	Thoma simplex, an infinite-dimensional compact space which is a kind
	of dual object to the infinite symmetric group. The aim of the paper
	is to introduce stochastic dynamics related to the z-measures. Namely,
	we construct a family of diffusion processes in the Toma simplex
	indexed by the same parameter z. Our diffusions are obtained from
	certain Markov chains on partitions of natural numbers n in a scaling
	limit as n goes to infinity. These Markov chains arise in a natural
	way, due to the approximation of the infinite symmetric group by
	the increasing chain of the finite symmetric groups. Each z-measure
	P_z serves as a unique invariant distribution for the corresponding
	diffusion process, and the process is ergodic with respect to P_z.
	Moreover, P_z is a symmetrizing measure, so that the process is reversible.
	We describe the spectrum of its generator and compute the associated
	(pre)Dirichlet form.},
	author = {Borodin, A. and Olshanski, G.},
	comments = {AMSTex, 33 pages. Version 2: minor changes, typos corrected, to appear in Prob. Theor. Rel. Fields},
	date-modified = {2018-02-28 19:38:39 +0000},
	journal = {Probab. Theory Relat. Fields},
	note = {arXiv:0706.1034 [math.PR]},
	number = {1},
	oai2identifier = {0706.1034},
	owner = {leo},
	pages = {281-318},
	reportno = {Preprint Series of SFB 701, University of Bielefeld, #07-035},
	timestamp = {2009.03.11},
	title = {Infinite-dimensional diffusions as limits of random walks on partitions},
	volume = {144},
	year = {2009},
	bdsk-url-1 = {http://arxiv.org/abs/0706.1034}}

@article{borodin2007asymptotics,
	author = {Borodin, A. and Olshanski, G.},
	journal = {Journal of Algebra},
	note = {arXiv:math/0610240},
	number = {1},
	pages = {40--60},
	publisher = {Elsevier},
	title = {{Asymptotics of Plancherel-type random partitions}},
	volume = {313},
	year = {2007}}

@article{Borodin2006,
	abstract = {We introduce and study a family of Markov processes on partitions.
	The processes preserve the so-called z-measures on partitions previously
	studied in connection with harmonic analysis on the infinite symmetric
	group. We show that the dynamical correlation functions of these
	processes have determinantal structure and we explicitly compute
	their correlation kernels. We also compute the scaling limits of
	the kernels in two different regimes. The limit kernels describe
	the asymptotic behavior of large rows and columns of the corresponding
	random Young diagrams, and the behavior of the Young diagrams near
	the diagonal. Our results show that recently discovered analogy between
	random partitions arising in representation theory and spectra of
	random matrices extends to the associated time-dependent models.},
	author = {Borodin, A. and Olshanski, G.},
	comments = {AMSTeX, 73 pages},
	date-modified = {2018-02-28 19:39:09 +0000},
	journal = {Probab. Theory Relat. Fields},
	note = {arXiv:math-ph/0409075},
	number = {1},
	oai2identifier = {math-ph/0409075},
	owner = {leo},
	pages = {84--152},
	timestamp = {2009.10.08},
	title = {Markov processes on partitions},
	volume = {135},
	year = {2006}}

@article{borodin2006meixner,
	author = {Borodin, A. and Olshanski, G.},
	journal = {Moscow Mathematical Journal},
	note = {arXiv:math/0609806 [math.PR]},
	number = {4},
	pages = {629--655},
	title = {{Meixner polynomials and random partitions}},
	volume = {6},
	year = {2006}}

@article{Borodin2005,
	abstract = {We study the asymptotics of certain measures on partitions (the so-called
	z-measures and their relatives) in two different regimes: near the
	diagonal of the corresponding Young diagram and in the intermediate
	zone between the diagonal and the edge of the Young diagram. We prove
	that in both cases the limit correlation functions have determinantal
	form with a correlation kernel which depends on two real parameters.
	In the first case the correlation kernel is discrete, and it has
	a simple expression in terms of the gamma functions. In the second
	case the correlation kernel is continuous and translationally invariant,
	and it can be a written as a ratio of two suitably scaled hyperbolic
	sines.},
	author = {Borodin, A. and Olshanski, G.},
	comments = {AMSTeX, 49 pages},
	date-modified = {2011-11-14 16:22:51 +0000},
	journal = {Adv. Math.},
	note = {arXiv:math-ph/0305043},
	number = {1},
	oai2identifier = {math-ph/0305043},
	owner = {leo},
	pages = {141--202},
	timestamp = {2009.10.21},
	title = {{Random partitions and the Gamma kernel}},
	volume = {194},
	year = {2005}}

@article{Borodin2005a,
	abstract = {The infinite-dimensional unitary group U(infinity) is the inductive
	limit of growing compact unitary groups U(N). In this paper we solve
	a problem of harmonic analysis on U(infinity) stated in the previous
	paper math/0109193. The problem consists in computing spectral decomposition
	for a remarkable 4-parameter family of characters of U(infinity).
	These characters generate representations which should be viewed
	as analogs of nonexisting regular representation of U(infinity).
	The spectral decomposition of a character of U(infinity) is described
	by the spectral measure which lives on an infinite-dimensional space
	Omega of indecomposable characters. The key idea which allows us
	to solve the problem is to embed Omega into the space of point configurations
	on the real line without 2 points. This turns the spectral measure
	into a stochastic point process on the real line. The main result
	of the paper is a complete description of the processes corresponding
	to our concrete family of characters. We prove that each of the processes
	is a determinantal point process. That is, its correlation functions
	have determinantal form with a certain kernel. Our kernels have a
	special `integrable' form and are expressed through the Gauss hypergeometric
	function. In simpler situations of harmonic analysis on infinite
	symmetric group and harmonic analysis of unitarily invariant measures
	on infinite hermitian matrices similar results were obtained in our
	papers math/9810015, math/9904010, math-ph/0010015.},
	author = {Alexei Borodin and Grigori Olshanski},
	comments = {AMSTeX, 88 pages},
	journal = {Ann. of Math.},
	number = {3},
	oai2identifier = {math/0109194},
	owner = {leo},
	pages = {1319--1422},
	timestamp = {2010.07.15},
	title = {Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes},
	volume = {161},
	year = {2005}}

@article{Borodin2005b,
	abstract = {We study certain probability measures on partitions of n=1,2,...,
	originated in representation theory, and demonstrate their connections
	with random matrix theory and multivariate hypergeometric functions.
	Our measures depend on three parameters including an analog of the
	beta parameter in random matrix models. Under an appropriate limit
	transition as n goes to infinity, our measures converge to certain
	limit measures, which are of the same nature as one-dimensional log-gas
	with arbitrary beta>0. The first main result says that averages of
	products of ``characteristic polynomials'' with respect to the limit
	measures are given by the multivariate hypergeometric functions of
	type (2,0). The second main result is a computation of the limit
	correlation functions for the even values of beta.},
	author = {Borodin, A. and Olshanski, G.},
	comments = {AMSTeX, 37 pages},
	date-modified = {2011-11-14 16:23:44 +0000},
	journal = {European J. Combin.},
	note = {arXiv:math-ph/0210048},
	number = {6},
	oai2identifier = {math-ph/0210048},
	owner = {leo},
	pages = {795--834},
	timestamp = {2010.08.10},
	title = {Z-measures on partitions and their scaling limits},
	volume = {26},
	year = {2005}}

@article{Borodin2000,
	abstract = {We construct examples of nonnegative harmonic functions on certain
	graded graphs: the Young lattice and its generalizations. Such functions
	first emerged in harmonic analysis on the infinite symmetric group.
	Our method relies on multivariate interpolation polynomials associated
	with Schur's S and P functions and with Jack symmetric functions.
	As a by-product, we compute certain Selberg-type integrals.},
	author = {Borodin, A. and Olshanski, G.},
	comments = {AMSTeX, 35 pages},
	date-modified = {2018-02-28 19:49:54 +0000},
	journal = {El. Jour. Combin.},
	note = {arXiv:math/9912124 [math.CO]},
	oai2identifier = {math/9912124},
	pages = {R28},
	title = {Harmonic functions on multiplicative graphs and interpolation polynomials},
	volume = {7},
	year = {2000},
	bdsk-url-1 = {http://arxiv.org/abs/math/9912124}}

@article{Borodin2000a,
	abstract = {We study a 3-parametric family of stochastic point processes on the
	one-dimensional lattice originated from a remarkable family of representations
	of the infinite symmetric group. We prove that the correlation functions
	of the processes are given by determinantal formulas with a certain
	kernel. The kernel can be expressed through the Gauss hypergeometric
	function; we call it the hypergeometric kernel. In a scaling limit
	our processes approximate the processes describing the decomposition
	of representations mentioned above into irreducibles. As we showed
	before, see math.RT/9810015, the correlation functions of these limit
	processes also have determinantal form with so-called Whittaker kernel.
	We show that the scaling limit of the hypergeometric kernel is the
	Whittaker kernel. The integral operator corresponding to the Whittaker
	kernel is an integrable operator as defined by Its, Izergin, Korepin,
	and Slavnov. We argue that the hypergeometric kernel can be considered
	as a kernel defining a `discrete integrable operator'. We also show
	that the hypergeometric kernel degenerates for certain values of
	parameters to the Christoffel-Darboux kernel for Meixner orthogonal
	polynomials. This fact is parallel to the degeneration of the Whittaker
	kernel to the Christoffel-Darboux kernel for Laguerre polynomials.},
	author = {Borodin, A. and Olshanski, G.},
	comments = {AMSTeX, 24 pages},
	date-modified = {2018-02-28 19:49:00 +0000},
	journal = {Math. Res. Lett.},
	note = {arXiv:math/9810015 [math.RT]},
	oai2identifier = {math/9810015},
	owner = {leo},
	pages = {799-816},
	timestamp = {2009.03.27},
	title = {Point processes and the infinite symmetric group},
	volume = {5},
	year = {1998}}

@article{borodin2006giambelli,
	author = {Borodin, A. and Olshanski, G. and Strahov, E.},
	journal = {Advances in Applied Mathematics},
	note = {arXiv:math-ph/0505021},
	number = {2},
	pages = {209--248},
	publisher = {Elsevier},
	title = {{Giambelli compatible point processes}},
	volume = {37},
	year = {2006}}

@article{BorodinPetrov2013Lect,
	author = {Borodin, A. and Petrov, L.},
	date-added = {2013-10-26 22:18:44 +0000},
	date-modified = {2014-10-14 16:02:59 +0000},
	journal = {Probab. Surv.},
	note = {arXiv:1310.8007 [math.PR]},
	pages = {1-58},
	title = {{Integrable probability: From representation theory to Macdonald processes}},
	volume = {11},
	year = {2014}}

@article{BorodinPetrov2013NN,
	author = {Borodin, A. and Petrov, L.},
	date-added = {2013-05-20 16:26:45 +0000},
	date-modified = {2018-12-15 10:39:57 -0500},
	journal = {Adv. Math.},
	note = {arXiv:1305.5501 [math.PR]},
	pages = {71-155},
	title = {{Nearest neighbor Markov dynamics on Macdonald processes}},
	volume = {300},
	year = {2016}}

@article{borodin2005eynard,
	author = {Borodin, A. and Rains, E.M.},
	date-modified = {2018-02-28 19:41:34 +0000},
	journal = {J. Stat. Phys},
	note = {arXiv:math-ph/0409059},
	number = {3},
	pages = {291--317},
	publisher = {Springer},
	title = {{Eynard--Mehta theorem, Schur process, and their Pfaffian analogs}},
	volume = {121},
	year = {2005}}

@article{borodin2010gibbs,
	author = {Borodin, A. and Shlosman, S.},
	date-modified = {2016-08-08 00:48:10 +0000},
	journal = {Commun. Math. Phys.},
	note = {arXiv:0804.0564 [math-ph]},
	number = {1},
	pages = {145--170},
	publisher = {Springer},
	title = {{Gibbs ensembles of nonintersecting paths}},
	volume = {293},
	year = {2010}}

@article{borodin2009correlation,
	author = {Borodin, A. and Strahov, E.},
	date-modified = {2016-08-02 03:01:21 +0000},
	issn = {0010-3616},
	journal = {Commun. Math. Phys.},
	note = {arXiv:0712.1693 [math-ph]},
	number = {3},
	pages = {933--977},
	publisher = {Springer},
	title = {{Correlation kernels for discrete symplectic and orthogonal ensembles}},
	volume = {286},
	year = {2009}}

@article{borodin2006averages,
	author = {Borodin, A. and Strahov, E.},
	date-modified = {2016-08-02 02:59:47 +0000},
	issn = {0010-3640},
	journal = {Comm. Pure Appl. Math.},
	note = {arXiv:math-ph/0407065},
	number = {2},
	pages = {161--253},
	publisher = {Wiley Online Library},
	title = {{Averages of characteristic polynomials in random matrix theory}},
	volume = {59},
	year = {2006}}

@article{BMRT2009BackWall,
	author = {Boutillier, C. and Mkrtchyan, S. and Reshetikhin, N. and Tingley, P.},
	date-added = {2012-02-05 15:11:49 +0000},
	date-modified = {2012-02-05 15:13:30 +0000},
	journal = {Annales Henri Poincare},
	note = {arXiv:0912.3968 [math-ph]},
	title = {Random skew plane partitions with a piecewise periodic back wall},
	year = {2011}}

@article{boyer1992characters,
	author = {Boyer, R.P.},
	date-added = {2012-10-21 22:43:40 +0000},
	date-modified = {2012-10-21 22:43:40 +0000},
	journal = {J. Operator Theory},
	pages = {281--307},
	title = {Characters and factor representations of the infinite dimensional classical groups},
	volume = {28},
	year = {1992}}

@article{Boyer1983,
	author = {Boyer, R.},
	date-added = {2011-06-15 10:56:54 +0400},
	date-modified = {2011-06-15 10:58:28 +0400},
	journal = {J. Operator Theory},
	pages = {205-236},
	title = {Infinite traces of {AF-algebras} and characters of {$U(\infty)$}},
	volume = {9},
	year = {1983}}

@article{Brauer1937,
	author = {Brauer, R.},
	date-added = {2011-06-15 12:27:06 +0400},
	date-modified = {2011-06-15 12:29:01 +0400},
	journal = {Ann. of Math.},
	number = {4},
	pages = {857-872},
	title = {On algebras which are connected with semisimple continuous groups},
	volume = {38},
	year = {1937}}

@article{Brender1976,
	author = {Brender, M.},
	date-added = {2011-06-15 13:53:38 +0400},
	date-modified = {2011-06-15 13:54:26 +0400},
	journal = {J. Algebra},
	pages = {302-314},
	title = {Spherical functions on the symmetric groups},
	volume = {42},
	year = {1976}}

@article{BreuerDuits2011StaircasePaths,
	author = {Breuer, J. and Duits, M.},
	date-added = {2011-08-03 07:01:12 +0000},
	date-modified = {2018-02-28 19:50:15 +0000},
	journal = {Electron. J. Probab.},
	note = {arXiv:1105.0388 [math.PR]},
	number = {60},
	pages = {24},
	title = {Nonintersecting paths with a staircase initial condition},
	year = {2012}}

@article{Brezin2010,
	abstract = {In a generalized Airy matrix model, a power $p$ replaces the cubic
	term of the Airy model introduced by Kontsevich. The parameter $p$
	corresponds to Witten's spin index in the theory of intersection
	numbers of moduli space of curves. A continuation in $p$ down to
	$p= -2$ yields a well studied unitary matrix model, which exhibits
	two different phases in the weak and strong coupling regions, with
	a third order critical point in-between. The application of duality
	and replica to the $p$-th Airy model allows one to recover both the
	weak and strong phases of the unitary model, and to establish some
	new results for these expansions. Therefore the unitary model is
	also indirectly a generating function for intersection numbers.},
	author = {E. Brezin and S. Hikami},
	comments = {18 page},
	oai2identifier = {1005.4730},
	owner = {leo},
	timestamp = {2010.05.30},
	title = {Duality and replicas for a unitary matrix model},
	year = {2010}}

@article{brundan2002projective,
	author = {Brundan, J. and Kleshchev, A.},
	journal = {Mathematische Zeitschrift},
	number = {1},
	pages = {27--68},
	publisher = {Springer},
	title = {{Projective representations of symmetric groups via Sergeev duality}},
	volume = {239},
	year = {2002}}

@article{BrycWesolowski2004qMeixner,
	author = {Bryc, W. and Wesolowski, J.},
	date-added = {2011-08-03 07:45:08 +0000},
	date-modified = {2011-08-03 07:45:51 +0000},
	note = {arXiv:math/0403016 [math.PR]},
	title = {Conditional moments of q-Meixner processes}}

@article{BufetovCLT,
	author = {Bufetov, A.},
	date-modified = {2016-02-16 02:53:07 +0000},
	journal = {Functional Analysis and Its Applications},
	note = {arXiv:1105.1519 [math.RT]},
	number = {2},
	owner = {leo},
	pages = {83-93},
	timestamp = {2013.07.21},
	title = {The central limit theorem for extremal characters of the infinite symmetric group},
	volume = {46},
	year = {2012}}

@article{GorinBufetov2013free,
	author = {Bufetov, A. and Gorin, V.},
	date-added = {2013-10-29 13:26:35 +0000},
	date-modified = {2016-08-02 02:52:55 +0000},
	journal = {Geometric And Functional Analysis},
	note = {arXiv:1311.5780 [math.RT]},
	number = {3},
	pages = {763-814},
	title = {{Representations of classical Lie groups and quantized free convolution}},
	volume = {25},
	year = {2015}}

@article{BufetovPetrov2014,
	author = {Bufetov, A. and Petrov, L.},
	date-added = {2013-08-10 13:58:43 +0000},
	date-modified = {2016-12-26 17:35:08 +0000},
	journal = {Selecta Math.},
	note = {arXiv:1402.1772 [math.PR]},
	number = {4},
	pages = {1271-1338},
	title = {{Law of Large Numbers for Infinite Random Matrices over a Finite Field}},
	volume = {21},
	year = {2015}}

@book{Bulinski2007,
	author = {Alexander Bulinski and Alexey Shashkin},
	editor = {Ole E. Barndorff-Nielsen},
	owner = {leo},
	publisher = {World Scientific, Singapore},
	timestamp = {2009.06.20},
	title = {{Limit Theorems for Associated Random Fields and Related Systems}},
	year = {2007}}

@conference{Burdzy-BM,
	author = {Krzysztof Burdzy},
	owner = {leo},
	timestamp = {2009.03.15},
	title = {Brownian Motion. A tutorial},
	year = {2006}}

@article{Butler2006,
	author = {Lynne Butler and Pat Flanigan},
	owner = {leo},
	timestamp = {2009.05.11},
	title = {Log-convexity of q-{C}atalan numbers},
	year = {2006}}

@article{CaiJing2011LaplaceJack,
	author = {Cai, W. and Jing, N.},
	date-added = {2011-08-03 08:06:54 +0000},
	date-modified = {2011-08-03 08:07:20 +0000},
	note = {arXiv:1101.5544 [math.QA]},
	title = {Applications of Laplace-Beltrami operator for Jack polynomials},
	year = {2011}}

@article{CaiJing2010VertexJack,
	author = {Cai, W. and Jing, N.},
	date-added = {2011-08-03 08:05:25 +0000},
	date-modified = {2011-08-03 08:06:14 +0000},
	note = {arXiv:1002.1350 [math.QA]},
	title = {On vertex operator realizations of Jack functions},
	year = {2010}}

@article{Calabrese_LeDoussal_Rosso,
	author = {Calabrese, P. and Le Doussal, P. and Rosso, A.},
	date-added = {2013-08-11 21:44:30 +0000},
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	number = {2},
	pages = {20002},
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	volume = {90},
	year = {2010}}

@article{Carlitz1964,
	author = {L. Carlitz and J. Riordan},
	journal = {Duke J. Math.},
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	volume = {31},
	year = {1964}}

@phdthesis{Carlton1999,
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	school = {UNIVERSITY OF CALIFORNIA Los Angeles},
	title = {{Applications of the two-parameter Poisson-Dirichlet distribution}},
	year = {1999}}

@article{CarmonaMolchanov,
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@article{Caron2006,
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@article{Cauchy1815,
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	date-added = {2013-10-25 23:57:09 +0000},
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	note = {Oeuvres, ser. 2, vol. 1, pp. 91-169.},
	number = {29-112},
	title = {{M\'emoire sur les fonctions qui ne peuvent obtenir que deux valeurs \'egales et de signes contraires par suite des transpositions op\'er\'es entre les variables qu'elles renferment}},
	volume = {10},
	year = {1815}}

@phdthesis{Chhaibi2013,
	author = {Chhaibi, R.},
	date-added = {2013-05-23 12:53:10 +0000},
	date-modified = {2013-05-23 12:53:47 +0000},
	note = {arXiv:1302.0902 [math.PR]},
	title = {{Littelmann path model for geometric crystals, Whittaker functions on Lie groups and Brownian motion}},
	year = {2013}}

@article{Chi1999,
	author = {Chi, Z.},
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	volume = {25},
	year = {1999}}

@article{ChowGessel2007DescentHyperoctahedral,
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	date-modified = {2011-08-04 06:31:10 +0000},
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	number = {3},
	pages = {275--301},
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	year = {2007}}

@article{Cigler2005,
	abstract = {In this note we show that various natural q-analogues of the Catalan
	numbers can be obtained in a uniform way. Furthermore we compute
	their Hankel determinants.},
	author = {Johann Cigler},
	comments = {10 pages},
	oai2identifier = {math/0507225},
	owner = {leo},
	timestamp = {2009.05.11},
	title = {q-{C}atalan numbers and q-{N}arayana polynomials},
	year = {2005}}

@article{Clarkson2005,
	author = {Kenneth L. Clarkson},
	owner = {leo},
	timestamp = {2009.04.03},
	title = {{Nearest-Neighbor Searching and Metric Space Dimensions}},
	year = {2005}}

@book{ODEs,
	author = {Coddington, E.A. and Levinson, N.},
	date-added = {2013-08-04 19:33:38 +0000},
	date-modified = {2013-08-04 19:34:34 +0000},
	publisher = {McGraw Hill},
	title = {{Theory of Ordinary Differential Equations}},
	year = {1955}}

@article{CohnKenyonPropp2000,
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	date-modified = {2018-02-28 19:42:56 +0000},
	journal = {Jour. AMS},
	note = {arXiv:math/0008220 [math.CO]},
	number = {2},
	pages = {297-346},
	title = {A variational principle for domino tilings},
	volume = {14},
	year = {2001}}

@article{CohnLarsenPropp,
	author = {Cohn, H. and Larsen, M. and Propp, J.},
	date-added = {2012-02-02 23:51:26 +0000},
	date-modified = {2012-02-02 23:52:56 +0000},
	journal = {New York J. Math},
	note = {arXiv:math/9801059 [math.CO]},
	pages = {137--165},
	title = {The shape of a typical boxed plane partition},
	volume = {4},
	year = {1998}}

@article{vuletic2009plane,
	author = {Corteel, S. and Savelief, C. and Vuleti{\'c}, M.},
	journal = {Imprint},
	title = {{Plane overpartitions and cylindric partitions}},
	year = {2009}}

@article{Corwin2012,
	author = {Corwin, I.},
	date-added = {2013-02-06 21:17:13 +0000},
	date-modified = {2013-02-06 21:18:17 +0000},
	note = {arXiv:1212.2267 [math.PR]},
	title = {Two ways to solve ASEP},
	year = {2012}}

@article{CorwinKPZ,
	author = {Corwin, I.},
	date-added = {2013-09-22 01:55:47 +0000},
	date-modified = {2020-05-22 23:23:23 -0400},
	journal = {Random Matrices Theory Appl.},
	note = {arXiv:1106.1596 [math.PR]},
	pages = {1130001},
	title = {{The Kardar-Parisi-Zhang equation and universality class}},
	volume = {1},
	year = {2012}}

@article{COSZ2011,
	author = {Corwin, I. and O'Connell, N. and Sepp{\"a}l{\"a}inen, T. and Zygouras, N.},
	date-added = {2013-04-19 00:54:30 +0000},
	date-modified = {2014-10-15 01:44:50 +0000},
	journal = {Duke J. Math.},
	note = {arXiv:1110.3489 [math.PR]},
	number = {3},
	pages = {513-563},
	title = {{Tropical Combinatorics and Whittaker functions}},
	volume = {163},
	year = {2014}}

@article{CorwinPetrov2013,
	author = {Corwin, I. and Petrov, L.},
	date-added = {2013-05-10 12:04:19 +0000},
	date-modified = {2018-02-28 19:41:34 +0000},
	journal = {J. Stat. Phys},
	note = {arXiv:1308.3124 [math.PR]},
	number = {4},
	pages = {1005-1026},
	title = {{The q-PushASEP: A New Integrable Model for Traffic in 1+1 Dimension}},
	volume = {160},
	year = {2015}}

@article{helbing2001trafficSurvey,
	author = {Helbing, D.},
	journal = {Reviews of modern physics},
	note = {arXiv:cond-mat/0012229 [cond-mat.stat-mech]},
	number = {4},
	pages = {1067--1141},
	publisher = {APS},
	title = {Traffic and related self-driven many-particle systems},
	volume = {73},
	year = {2001}}

@article{CorwinSeppalainenShen2014,
	author = {Corwin, I. and Sepp\"al\"ainen, T. and Shen, H.},
	date-modified = {2018-02-28 19:41:34 +0000},
	journal = {J. Stat. Phys},
	note = {arXiv:1409.1794 [math.PR]},
	number = {4},
	pages = {1027-1053},
	title = {{The strict-weak lattice polymer}},
	volume = {160},
	year = {2015}}

@article{Cox85a,
	author = {Cox, J.C. and Ingersoll, J.E. and Ross, S.A.},
	date-added = {2011-10-10 13:05:56 +0000},
	date-modified = {2011-10-10 13:05:56 +0000},
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	number = {2},
	pages = {363-384},
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	volume = {53},
	year = {1985}}

@article{Cox85b,
	author = {Cox, J.C. and Ingersoll, J.E. and Ross, S.A.},
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	date-modified = {2011-10-10 13:06:17 +0000},
	journal = {Econometrica},
	number = {2},
	pages = {385-407},
	title = {A Theory of the Term Structure of Interest Rates},
	volume = {53},
	year = {1985}}

@article{Csaki2008,
	abstract = {We prove strong invariance principle between a transient Bessel process
	and a certain nearest neighbor (NN) random walk that is constructed
	from the former by using stopping times. It is also shown that their
	local times are close enough to share the same strong limit theorems.
	It is shown furthermore, that if the difference between the distributions
	of two NN random walks are small, then the walks themselves can be
	constructed so that they are close enough. Finally, some consequences
	concerning strong limit theorems are discussed.},
	author = {Endre Cs{\'a}ki and Ant{\'o}nia F{\"o}ldes and P{\'a}l R{\'e}v{\'e}sz},
	eprint = {0802.0778},
	oai2identifier = {0802.0778},
	owner = {leo},
	timestamp = {2009.04.03},
	title = {Transient nearest neighbor random walk and Bessel process},
	url = {http://arxiv.org/abs/0802.0778},
	year = {2008},
	bdsk-url-1 = {http://arxiv.org/abs/0802.0778}}

@article{CurryShoenberg1966IV,
	author = {H. Curry and I. Schoenberg},
	date-added = {2012-10-23 13:32:32 +0000},
	date-modified = {2012-10-23 13:33:51 +0000},
	journal = {Journal d'Analyse Math{\'e}matique},
	number = {1},
	pages = {71-107},
	title = {{On P\'olya frequency functions IV: The fundamental spline functions and their limits}},
	volume = {17},
	year = {1966}}

@article{date1982transformation,
	author = {Date, E. and Jimbo, M. and Kashiwara, M. and Miwa, T.},
	journal = {Physica D},
	pages = {343--365},
	title = {{Transformation groups for soliton equations. IV. A new hierarchy of soliton equations of KP-type}},
	volume = {4},
	year = {1982}}

@incollection{Dawson1991,
	address = {Berlin},
	author = {Dawson, D.},
	booktitle = {\'{E}cole d'\'{E}t{\'e} de {P}robabilit{\'e}s de {S}aint-{F}lour {XXI}---1991},
	date-added = {2011-11-14 16:31:40 +0000},
	date-modified = {2011-12-03 03:21:10 +0000},
	pages = {1--260},
	publisher = {Springer},
	series = {Lecture Notes in Math.},
	title = {Measure-valued {M}arkov processes},
	volume = {1541},
	year = {1993},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=1242575}}

@article{Dawson2009,
	author = {Donald A. Dawson},
	owner = {leo},
	timestamp = {2009.08.04},
	title = {{PIMS-UBC Summer School 2009 Lecture Notes}},
	year = {2009}}

@article{Deerwester1990,
	author = {Deerwester, S. and Dumais, S.T. and Furnas, G.W. and Landauer, T.K. and Harshman, R.},
	journal = {Journal of the American society for information science},
	number = {6},
	pages = {391--407},
	publisher = {Citeseer},
	title = {{Indexing by latent semantic analysis}},
	volume = {41},
	year = {1990}}

@incollection{deift1999integrable,
	author = {Deift, P.},
	booktitle = {Differential operators and spectral theory: M. Sh. Birman's 70th Anniversay Collection},
	journal = {Differential operators and spectral theoryM. Sh. Birman's 70th Anniversay Collection},
	pages = {69},
	publisher = {Transl. AMS},
	title = {{Integrable operators}},
	year = {1999}}

@article{Delong2010,
	abstract = {We investigate solutions of backward stochastic differential equations
	(BSDE) with time delayed generators driven by Brownian motions and
	Poisson random measures, that constitute the two components of a
	Levy process. In this new type of equations, the generator can depend
	on the past values of a solution, by feeding them back into the dynamics
	with a time lag. For such time delayed BSDE, we prove existence and
	uniqueness of solutions provided we restrict on a sufficiently small
	time horizon or the generator possesses a sufficiently small Lipschitz
	constant. We study differentiability in the variational or Malliavin
	sense and derive equations that are satisfied by the Malliavin gradient
	processes. On the chosen stochastic basis this addresses smoothness
	both with respect to the continuous part of our Levy process in terms
	of the classical Malliavin derivative for Hilbert space valued random
	variables, as well as with respect to the pure jump component for
	which it takes the form of an increment quotient operator related
	to the Picard difference operator.},
	author = {Delong, L. and Imkeller, P.},
	eprint = {1005.4702},
	oai2identifier = {1005.4702},
	owner = {leo},
	timestamp = {2010.05.30},
	title = {On Malliavin's differentiability of BSDE with time delayed generators driven by Brownian motions and Poisson random measures},
	year = {2010}}

@article{Delong2010a,
	abstract = {We deal with backward stochastic differential equations with time
	delayed generators. In this new type of equations, a generator at
	time t can depend on the values of a solution in the past, weighted
	with a time delay function for instance of the moving average type.
	We prove existence and uniqueness of a solution for a sufficiently
	small time horizon or for a sufficiently small Lipschitz constant
	of a generator. We give examples of BSDE with time delayed generators
	that have multiple solutions or that have no solutions. We show for
	some special class of generators that existence and uniqueness may
	still hold for an arbitrary time horizon and for arbitrary Lipschitz
	constant. This class includes linear time delayed generators, which
	we study in more detail. We are concerned with different properties
	of a solution of a BSDE with time delayed generator, including the
	inheritance of boundedness from the terminal condition, the comparison
	principle, the existence of a measure solution and the BMO martingale
	property. We give examples in which they may fail.},
	author = {Delong, L. and Imkeller, P.},
	eprint = {1005.4701},
	oai2identifier = {1005.4701},
	owner = {leo},
	timestamp = {2010.05.30},
	title = {Backward stochastic differential equations with time delayed generators - results and counterexamples},
	year = {2010}}

@article{Delvaux2008,
	abstract = {We consider n non-intersecting Brownian motions with two fixed starting
	positions and two fixed ending positions in the large n limit. We
	show that in case of 'large separation' between the endpoints, the
	particles are asymptotically distributed in two separate groups,
	with no interaction between them, as one would intuitively expect.
	We give a rigorous proof using the Riemann-Hilbert formalism. In
	the case of 'critical separation' between the endpoints we are led
	to a model Riemann-Hilbert problem associated to the Hastings-McLeod
	solution of the Painleve II equation. We show that the Painleve II
	equation also appears in the large n asymptotics of the recurrence
	coefficients of the multiple Hermite polynomials that are associated
	with the Riemann-Hilbert problem.},
	author = {Steven Delvaux and Arno B. J. Kuijlaars},
	comments = {75 pages, 13 figures},
	eprint = {0809.1000},
	note = {arXiv:0809.1000 [math.CV]},
	oai2identifier = {0809.1000},
	owner = {leo},
	timestamp = {2010.10.01},
	title = {A phase transition for non-intersecting Brownian motions, and the Painleve II equation},
	year = {2008}}

@article{E.P.vanDenBanH.Schlichtkrull,
	author = {van Den Ban, E.P. and Schlichtkrull, H.},
	date-added = {2013-09-21 17:43:10 +0000},
	date-modified = {2013-09-21 17:43:46 +0000},
	journal = {Ann. Math.},
	pages = {267--364},
	title = {{The most continuous part of the Plancherel decomposition for a reductive symmetric space}},
	volume = {145},
	year = {1997}}

@article{Desrosiers2011Laguerre,
	author = {Desrosiers, P. and Hallnas, M.},
	date-added = {2011-07-06 16:43:54 +0400},
	date-modified = {2011-07-06 16:44:51 +0400},
	note = {arXiv:1103.4593 [math.QA]},
	title = {{Hermite and Laguerre symmetric functions associated with operators of Calogero-Moser-Sutherland type}},
	year = {2011}}

@article{Destainville1998Lozenge,
	author = {Destainville, N.},
	date-added = {2012-02-03 00:04:59 +0000},
	date-modified = {2012-02-03 00:05:44 +0000},
	journal = {J. Phys. A: Math. Gen.},
	pages = {6123--6139},
	title = {Entropy and boundary conditions in random rhombus tilings},
	volume = {31},
	year = {1998}}

@article{DMB1997Lozenge,
	author = {Destainville, N. and Mosseri, R. and F. Bailly},
	date-added = {2012-02-03 00:03:12 +0000},
	date-modified = {2012-02-03 00:04:37 +0000},
	journal = {J. Stat. Phys.},
	number = {3/4},
	pages = {697--754},
	title = {Configurational entropy of codimension-one tilings and directed membranes},
	volume = {87},
	year = {1997}}

@book{Dey1998,
	author = {Dey, D. and Mueller, P. and Sinha, D.},
	publisher = {Springer New York},
	title = {{Practical nonparametric and semiparametric Bayesian statistics}},
	year = {1998}}

@article{DiFrancescoReshetikhin2009FreeBound,
	author = {Di Francesco, P. and Reshetikhin, N.},
	date-added = {2011-08-03 06:58:57 +0000},
	date-modified = {2011-08-03 07:00:01 +0000},
	note = {arXiv:0908.1630 [math-ph]},
	title = {Asymptotic shapes with free boundaries}}

@article{DiaconisFill1990,
	author = {Diaconis, P. and Fill, J.A.},
	date-added = {2013-01-16 17:39:25 +0000},
	date-modified = {2016-10-23 14:36:08 +0000},
	journal = {Ann. Probab.},
	pages = {1483-1522},
	title = {Strong Stationary Times via a New Form of Duality},
	volume = {18},
	year = {1990}}

@article{Dickman1930,
	author = {Dickman, K.},
	journal = {Ark. Mat. Astr. Fys},
	pages = {1-14},
	title = {{On the frequency of numbers containing prime factors of a certain relative magnitude}},
	volume = {22},
	year = {1930}}

@article{VanDiejen2013_1,
	author = {van Diejen, J.F. and Emsiz, E.},
	date-added = {2013-08-12 11:50:42 +0000},
	date-modified = {2013-08-14 03:17:54 +0000},
	journal = {Letters in Mathematical Physics},
	note = {arXiv:1308.2242 [math-ph]},
	number = {1},
	pages = {103--113},
	title = {{The semi-infinite q-Boson system with boundary interaction}},
	volume = {104},
	year = {2014}}

@article{VanDiejen2013_2,
	author = {van Diejen, J.F. and Emsiz, E.},
	date-added = {2013-08-12 11:47:18 +0000},
	date-modified = {2013-08-14 03:17:49 +0000},
	journal = {Journal of Functional Analysis},
	note = {arXiv:1308.2237 [math-ph]},
	number = {9},
	pages = {5801--5817},
	title = {{Diagonalization of the infinite q-Boson}},
	volume = {266},
	year = {2014}}

@article{Donnelly1999,
	author = {Donnelly, P. and Kurtz, T.G.},
	journal = {Annals of Applied Probability},
	number = {4},
	pages = {1091--1148},
	publisher = {Institute of Mathematical Statistics},
	title = {{Genealogical processes for Fleming-Viot models with selection and recombination}},
	volume = {9},
	year = {1999}}

@article{Donnelly1999a,
	author = {Donnelly, P. and Kurtz, T.G.},
	date-modified = {2018-02-28 19:46:40 +0000},
	journal = {Ann. Probab.},
	number = {1},
	pages = {166--205},
	publisher = {Institute of Mathematical Statistics},
	title = {{Particle representations for measure-valued population models}},
	volume = {27},
	year = {1999}}

@article{Donnelly1996,
	author = {Donnelly, P. and Kurtz, T.G.},
	date-modified = {2018-02-28 19:46:40 +0000},
	journal = {Ann. Probab.},
	number = {2},
	pages = {698--742},
	publisher = {Institute of Mathematical Statistics},
	title = {{A countable representation of the Fleming-Viot measure-valued diffusion}},
	volume = {24},
	year = {1996}}

@article{DotsenkoTW_onedim,
	author = {Dotsenko, V.},
	journal = {Euro. Phys. Lett.},
	note = {arXiv:1003.4899 [cond-mat.dis-nn]},
	number = {20003},
	title = {{Bethe ansatz derivation of the Tracy-Widom distribution for one-dimensional directed polymers}},
	volume = {90},
	year = {2010}}

@article{Dotsenko2010_universal,
	author = {Dotsenko, V.},
	journal = {Physics Uspekhi},
	note = {arXiv:1009.3116 [cond-mat.stat-mech]},
	number = {3},
	pages = {259--280},
	title = {Universal randomness},
	volume = {54},
	year = {2011}}

@article{Dotsenko,
	author = {Dotsenko, V.},
	date-added = {2013-08-11 21:52:06 +0000},
	date-modified = {2013-08-12 11:42:11 +0000},
	journal = {Journal of Statistical Mechanics: Theory and Experiment},
	note = {arXiv:1004.4455 [cond-mat.dis-nn]},
	number = {07},
	pages = {P07010},
	title = {{Replica Bethe ansatz derivation of the Tracy-Widom distribution of the free energy fluctuations in one-dimensional directed polymers}},
	year = {2010}}

@article{Duits2011GFF,
	author = {Duits, M.},
	date-added = {2012-02-03 00:55:34 +0000},
	date-modified = {2014-10-12 13:29:30 +0000},
	journal = {Comm. Pure Appl. Math.},
	note = {arXiv:1105.4656 [math-ph]},
	number = {4},
	pages = {600-643},
	title = {{The Gaussian free field in an interlacing particle system with two jump rates}},
	volume = {66},
	year = {2013}}

@article{dyson1970correlations,
	author = {Dyson, F.J.},
	date-modified = {2016-08-02 03:01:02 +0000},
	issn = {0010-3616},
	journal = {Commun. Math. Phys.},
	number = {3},
	pages = {235--250},
	publisher = {Springer},
	title = {{Correlations between eigenvalues of a random matrix}},
	volume = {19},
	year = {1970}}

@article{Dyson1962_III,
	author = {Dyson, F.J.},
	date-added = {2013-10-12 17:48:48 +0000},
	date-modified = {2013-10-12 17:49:11 +0000},
	journal = {Jour. Math. Phys.},
	number = {166},
	title = {{Statistical Theory of the Energy Levels of Complex Systems. III}},
	volume = {3},
	year = {1962}}

@article{dyson1962brownian,
	author = {Dyson, F.J.},
	date-modified = {2011-09-10 14:58:46 +0000},
	journal = {Jour. Math. Phys.},
	number = {6},
	pages = {1191--1198},
	title = {{A Brownian motion model for the eigenvalues of a random matrix}},
	volume = {3},
	year = {1962}}

@article{Dyson1972,
	author = {Freeman J. Dyson},
	journal = {J. Math. Phys.},
	owner = {leo},
	timestamp = {2009.12.05},
	title = {A Class of Matrix Ensembles},
	volume = {13},
	year = {1972}}

@article{Edrei53,
	author = {Edrei, A.},
	date-added = {2012-06-26 06:21:45 +0000},
	date-modified = {2018-02-28 19:44:38 +0000},
	journal = {Trans. AMS},
	pages = {367-383},
	title = {On the generating function of a doubly infinite, totally positive sequence},
	volume = {74},
	year = {1953}}

@article{Edrei1952,
	author = {Edrei, A.},
	date-added = {2011-11-14 16:35:13 +0000},
	date-modified = {2011-11-14 16:35:42 +0000},
	fjournal = {Journal d'Analyse Math{\'e}matique},
	issn = {0021-7670},
	journal = {J. Analyse Math.},
	pages = {104--109},
	title = {On the generating functions of totally positive sequences. {II}},
	volume = {2},
	year = {1952},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=0053175}}

@article{Eie83,
	author = {Eie, B.},
	coden = {SJSADG},
	date-added = {2011-11-14 16:46:17 +0000},
	date-modified = {2011-11-14 16:46:35 +0000},
	fjournal = {Scandinavian Journal of Statistics. Theory and Applications},
	issn = {0303-6898},
	journal = {Scand. J. Statist.},
	number = {3},
	pages = {247--250},
	title = {The generalized {B}essel process corresponding to an Ornstein-Uhlenbeck process},
	volume = {10},
	year = {1983},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=732920}}

@article{EllisKhovanov2011OddSymm,
	author = {Ellis, A.P. and Khovanov, M.},
	date-added = {2011-08-03 08:08:04 +0000},
	date-modified = {2011-08-03 08:08:48 +0000},
	note = {arXiv:1107.5610 [math.QA]},
	title = {The Hopf algebra of odd symmetric functions},
	year = {2011}}

@book{engen1978stochastic,
	author = {Engen, S.},
	publisher = {Chapman \& Hall},
	title = {{Stochastic abundance models: with emphasis on biological communities and species diversity}},
	year = {1978}}

@article{Erdos2010,
	abstract = {We study the universality of spectral statistics of large random matrices.
	We consider $N\times N$ symmetric, hermitian or quaternion self-dual
	random matrices with independent, identically distributed entries
	(Wigner matrices) where the probability distribution for each matrix
	element is given by a measure $\nu$ with a subexponential decay.
	Our main result is that the correlation functions of the local eigenvalue
	statistics in the bulk of the spectrum coincide with those of the
	Gaussian Orthogonal Ensemble (GOE), the Gaussian Unitary Ensemble
	(GUE) and the Gaussian Symplectic Ensemble (GSE), respectively, in
	the limit $N\to \infty$. Our approach is based on the study of the
	Dyson Brownian motion via a related new dynamics, the local relaxation
	flow. As a main input, we establish that the density of eigenvalues
	converges to the Wigner semicircle law and this holds even down to
	the smallest possible scale, and, moreover, we show that eigenvectors
	are fully delocalized. These results hold even without the condition
	that the matrix elements are identically distributed, only independence
	is used. In fact, we give strong estimates on the matrix elements
	of the Green function as well that imply that the local statistics
	of any two ensembles in the bulk are identical if the first four
	moments of the matrix elements match. Universality at the spectral
	edges requires matching only two moments. We also prove a Wegner
	type estimate and that the eigenvalues repel each other on arbitrarily
	small scales.},
	author = {Erd{\H{o}}s, L.},
	comments = {111 pages},
	date-modified = {2016-08-02 20:37:49 +0000},
	eprint = {1004.0861},
	oai2identifier = {1004.0861},
	owner = {leo},
	timestamp = {2010.11.01},
	title = {Universality of Wigner random matrices: a Survey of Recent Results},
	year = {2010}}

@article{Escobar1995,
	author = {Escobar, M.D. and West, M.},
	journal = {Journal of the american statistical association},
	number = {430},
	publisher = {American Statistical Association},
	title = {{Bayesian Density Estimation and Inference Using Mixtures.}},
	volume = {90},
	year = {1995}}

@book{Etheridge:2000fk,
	address = {Providence, RI},
	author = {Etheridge, A.},
	date-added = {2011-11-14 16:49:05 +0000},
	date-modified = {2011-11-14 16:49:27 +0000},
	isbn = {0-8218-2706-5},
	pages = {xii+187},
	publisher = {American Mathematical Society},
	series = {University Lecture Series},
	title = {An introduction to superprocesses},
	volume = {20},
	year = {2000},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=1779100}}

@article{Etheridge2009,
	author = {A.M. Etheridge and R.C. Griffiths},
	journal = {Theoretical Population Biology},
	owner = {leo},
	pages = {320-330},
	timestamp = {2009.08.19},
	title = {A coalescent dual process in a {M}oran model with genic selection},
	volume = {75},
	year = {2009}}

@article{etheridge1991note,
	author = {Etheridge, A. and March, P.},
	coden = {PTRFEU},
	date-added = {2011-11-14 13:41:06 +0000},
	date-modified = {2018-02-28 19:39:09 +0000},
	fjournal = {Probability Theory and Related Fields},
	journal = {Probab. Theory Relat. Fields},
	number = {2},
	pages = {141--147},
	title = {A note on superprocesses},
	volume = {89},
	year = {1991},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=1110534}}

@article{Ethier1993b,
	author = {Ethier, SN and Griffiths, RC},
	date-modified = {2016-05-04 16:38:26 +0000},
	journal = {{Ann. Probab.}},
	number = {3},
	pages = {1571--1590},
	publisher = {Institute of Mathematical Statistics},
	title = {{The transition function of a Fleming-Viot process}},
	volume = {21},
	year = {1993}}

@article{ethier1998coupling,
	author = {Ethier, SN and Kurtz, T.G.},
	date-modified = {2018-02-28 19:46:40 +0000},
	issn = {0091-1798},
	journal = {Ann. Probab.},
	number = {2},
	pages = {533--561},
	publisher = {Institute of Mathematical Statistics},
	title = {{Coupling and ergodic theorems for Fleming-Viot processes}},
	volume = {26},
	year = {1998}}

@book{Ethier1986,
	author = {Ethier, S.N. and Kurtz, T.G.},
	date-modified = {2011-11-14 16:47:17 +0000},
	owner = {leo},
	publisher = {Wiley-Interscience, New York},
	timestamp = {2009.03.26},
	title = {Markov processes: {C}haracterization and convergence},
	year = {1986}}

@article{Ethier1981,
	author = {Ethier, S.N. and Kurtz, T.G.},
	journal = {Advances in Applied Probability},
	number = {3},
	owner = {leo},
	pages = {429-452},
	timestamp = {2009.07.09},
	title = {{The Infinitely-Many-Neutral-Alleles Diffusion Model}},
	volume = {13},
	year = {1981}}

@article{Ethier1992,
	author = {S. N. Ethier},
	journal = {J. Appl. Prob.},
	number = {3},
	owner = {leo},
	pages = {487-498},
	timestamp = {2009.04.05},
	title = {{Eigenstructure of the Infinitely-Many-Neutral-Alleles Diffusion Model}},
	volume = {29},
	year = {1992}}

@article{Ethier1990,
	author = {Stewart N. Ethier},
	journal = {Advances in Applied Probability},
	number = {1},
	owner = {leo},
	pages = {1-24},
	timestamp = {2009.08.30},
	title = {{The Infinitely-Many-Neutral-Alleles Diffusion Model Model with Ages}},
	volume = {22},
	year = {1990}}

@article{Ethier1993a,
	author = {Stewart N. Ethier and Thomas G. Kurtz},
	journal = {Stochastic Processes and their Applications},
	number = {1},
	owner = {leo},
	pages = {1-27},
	timestamp = {2009.08.18},
	title = {Convergence to {F}leming-{V}iot processes in the weak atomic topology},
	volume = {54},
	year = {1994}}

@article{Ethier1993,
	author = {Stewart N. Ethier and Thomas G. Kurtz},
	journal = {SIAM J. Control and Optimization},
	number = {2},
	owner = {leo},
	pages = {345-386},
	timestamp = {2009.08.05},
	title = {{Fleming-Viot processes in population genetics}},
	volume = {31},
	year = {1993}}

@article{Ethier1987,
	author = {Stewart N. Ethier and Thomas G. Kurtz},
	journal = {Lecture Notes in Biomathematics},
	owner = {leo},
	pages = {72-86},
	timestamp = {2009.09.20},
	title = {The infinitely-many-alleles model with selection as a measure-valued diffusion},
	volume = {70},
	year = {1987}}

@article{EvansPerkins1990nonextinction,
	author = {Evans, Steven N. and Perkins, Edwin},
	coden = {ISJMAP},
	date-added = {2011-11-14 13:38:30 +0000},
	date-modified = {2011-11-14 13:38:44 +0000},
	doi = {10.1007/BF02773751},
	fjournal = {Israel Journal of Mathematics},
	issn = {0021-2172},
	journal = {Israel J. Math.},
	mrclass = {60J80 (60G57)},
	mrnumber = {1088825 (92d:60089)},
	mrreviewer = {Luis G. Gorostiza},
	number = {3},
	pages = {329--337},
	title = {{Measure-valued Markov branching processes conditioned on nonextinction}},
	url = {http://dx.doi.org/10.1007/BF02773751},
	volume = {71},
	year = {1990},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=1088825},
	bdsk-url-2 = {http://dx.doi.org/10.1007/BF02773751}}

@article{Ewens1972,
	author = {Warren Ewens},
	journal = {Theoretical Population Biology},
	owner = {leo},
	pages = {87-112},
	timestamp = {2010.01.12},
	title = {The sampling theory of selectively neutral alleles},
	volume = {3},
	year = {1972}}

@book{Ewens1979,
	author = {W. J. Ewens},
	owner = {leo},
	publisher = {Springer-Verlag, Berlin},
	timestamp = {2009.03.27},
	title = {{Mathematical Population Genetics}},
	year = {1979}}

@article{eynard1998matrices,
	author = {Eynard, B. and Mehta, M.L.},
	date-modified = {2018-06-13 15:33:18 +0000},
	journal = {J. Phys. A},
	pages = {4449--4456},
	publisher = {IOP Publishing},
	title = {{Matrices coupled in a chain: I. Eigenvalue correlations}},
	volume = {31},
	year = {1998}}

@article{Favaro2007,
	author = {Favaro, S. and Ruggiero, M. and Span{\c{n}}, D. and Walker, S.G.},
	journal = {ICER Working Papers-Applied Mathematics Series},
	publisher = {ICER-International Centre for Economic Research},
	title = {{The Neutral Population Model and Bayesian Nonparametrics}},
	year = {2007}}

@article{Feigin:etal:2010fk,
	abstract = {We begin a study of the representation theory of quantum continuous
	$\mathfrak{gl}_\infty$, which we denote by $\mathcal E$. This algebra
	depends on two parameters and is a deformed version of the enveloping
	algebra of the Lie algebra of difference operators acting on the
	space of Laurent polynomials in one variable. Fundamental representations
	of $\mathcal E$ are labeled by a continuous parameter $u\in {\mathbb
	C}$. The representation theory of $\mathcal E$ has many properties
	familiar from the representation theory of $\mathfrak{gl}_\infty$:
	vector representations, Fock modules, semi-infinite constructions
	of modules. Using tensor products of vector representations, we construct
	surjective homomorphisms from $\mathcal E$ to spherical double affine
	Hecke algebras $S\ddot H_N$ for all $N$. A key step in this construction
	is an identification of a natural bases of the tensor products of
	vector representations with Macdonald polynomials. We also show that
	one of the Fock representations is isomorphic to the module constructed
	earlier by means of the $K$-theory of Hilbert schemes.},
	author = {B. Feigin and E. Feigin and M. Jimbo and T. Miwa and E. Mukhin},
	date-added = {2011-11-02 23:11:04 +0000},
	date-modified = {2011-11-02 23:11:24 +0000},
	eprint = {1002.3100v1},
	title = {Quantum continuous $\mathfrak{gl}_\infty$: Semi-infinite construction of representations},
	url = {http://arxiv.org/abs/1002.3100v1},
	year = {2010},
	bdsk-url-1 = {http://arxiv.org/abs/1002.3100v1}}

@incollection{FeiginFuchs1990Virasoro,
	address = {New York},
	author = {Feigin, B. L. and Fuchs, D. B.},
	booktitle = {Representation of {L}ie groups and related topics},
	date-added = {2011-11-07 17:24:06 +0000},
	date-modified = {2011-11-08 13:42:21 +0000},
	mrclass = {17B68 (81R10)},
	mrnumber = {1104280 (92f:17034)},
	mrreviewer = {Joris Van der Jeugt},
	pages = {465--554},
	publisher = {Gordon and Breach},
	series = {Adv. Stud. Contemp. Math.},
	title = {Representations of the {V}irasoro algebra},
	volume = {7},
	year = {1990},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=1104280}}

@incollection{FeiginFuchs1984Virasoro,
	address = {Berlin},
	author = {Feigin, B. L. and Fuchs, D. B.},
	booktitle = {Topology ({L}eningrad, 1982)},
	date-added = {2011-11-07 17:24:16 +0000},
	date-modified = {2011-11-08 13:42:32 +0000},
	doi = {10.1007/BFb0099939},
	mrclass = {17B10 (17B35 17B67)},
	mrnumber = {770243 (86g:17004)},
	mrreviewer = {Alvany Rocha-Caridi},
	pages = {230--245},
	publisher = {Springer},
	series = {Lecture Notes in Math.},
	title = {Verma modules over the {V}irasoro algebra},
	url = {http://dx.doi.org/10.1007/BFb0099939},
	volume = {1060},
	year = {1984},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=770243},
	bdsk-url-2 = {http://dx.doi.org/10.1007/BFb0099939}}

@book{FellerProb,
	author = {Feller, W.},
	date-added = {2012-09-09 17:37:08 +0000},
	date-modified = {2012-09-09 17:40:31 +0000},
	publisher = {Wiley},
	title = {{An Introduction to Probability Theory and Its Applications. Vol. 1-2}},
	year = {1968, 1971}}

@book{Feng2010book,
	author = {Feng, S.},
	owner = {leo},
	publisher = {Springer},
	timestamp = {2010.11.03},
	title = {{The Poisson-Dirichlet distributions and related topics: Models and asymptotic behaviours}},
	year = {2010}}

@article{Feng2009a,
	abstract = {The two-parameter Poisson-Dirichlet distribution is the law of a sequence
	of decreasing nonnegative random variables with total sum one. It
	can be constructed from stable and Gamma subordinators with the two-parameters,
	$\alpha$ and $\theta$, corresponding to the stable component and
	Gamma component respectively. The moderate deviation principles are
	established for the two-parameter Poisson-Dirichlet distribution
	and the corresponding homozygosity when $\theta$ approaches infinity,
	and the large deviation principle is established for the two-parameter
	Poisson-Dirichlet distribution when both $\alpha$ and $\theta$ approach
	zero.},
	author = {Shui Feng and Fuqing Gao},
	eprint = {0906.2217},
	oai2identifier = {0906.2217},
	owner = {leo},
	timestamp = {2009.08.05},
	title = {Asymptotic {R}esults for the {T}wo-parameter {P}oisson-{D}irichlet {D}istribution},
	year = {2009}}

@article{Feng2009,
	abstract = {The two parameter Poisson-Dirichlet distribution $PD(\alpha,\theta)$
	is the distribution of an infinite dimensional random discrete probability.
	It is a generalization of Kingman's Poisson-Dirichlet distribution.
	The two parameter Dirichlet process $\Pi_{\alpha,\theta,\nu_0}$ is
	the law of a pure atomic random measure with masses following the
	two parameter Poisson-Dirichlet distribution. In this article we
	focus on the construction and the properties of the infinite dimensional
	symmetric diffusion processes with respective symmetric measures
	$PD(\alpha,\theta)$ and $\Pi_{\alpha,\theta,\nu_0}$. The methods
	used come from the theory of Dirichlet forms.},
	author = {Shui Feng and Wei Sun},
	comments = {24 pages},
	date-modified = {2018-02-28 19:39:25 +0000},
	eprint = {0903.0623},
	journal = {Probab. Theory Relat. Fields},
	oai2identifier = {0903.0623},
	owner = {leo},
	timestamp = {2009.06.13},
	title = {Some {D}iffusion {P}rocesses {A}ssociated With {T}wo {P}arameter {P}oisson-{D}irichlet {D}istribution and {D}irichlet {P}rocess},
	year = {2009}}

@article{feng2010functional,
	author = {Feng, S. and Sun, W. and Wang, F.Y. and Xu, F.},
	issn = {0022-1236},
	journal = {Journal of Functional Analysis},
	publisher = {Elsevier},
	title = {{Functional inequalities for the two-parameter extension of the infinitely-many-neutral-alleles diffusion}},
	year = {2010}}

@article{Feng2007,
	author = {Shui Feng and Feng-Yu Wang},
	comments = {14 pages},
	eprint = {0711.1887},
	oai2identifier = {0711.1887},
	owner = {leo},
	timestamp = {2009.06.14},
	title = {A Class of Infinite Dimensional Diffusion Processes with Connection to Population Genetics},
	year = {2007}}

@article{Ferguson1973,
	author = {Thomas S. Ferguson},
	journal = {The Annals of Statistics},
	number = {2},
	owner = {leo},
	pages = {209-230},
	timestamp = {2010.01.12},
	title = {A Bayesian Analysis of Some Nonparametric Problems},
	volume = {1},
	year = {1973}}

@other{Ferrari_anim,
	author = {Ferrari, P.},
	date-added = {2013-10-13 14:59:29 +0000},
	date-modified = {2013-10-13 15:02:41 +0000},
	note = {\url{http://wt.iam.uni-bonn.de/ferrari/research/anisotropickpz/}},
	title = {{Java animation of a growth model in the anisotropic KPZ class in 2 + 1 dimensions}},
	urldate = {2008},
	year = {2008}}

@article{ferrari2004polynuclear,
	author = {Ferrari, P.},
	date-modified = {2016-08-02 03:00:53 +0000},
	journal = {Commun. Math. Phys.},
	note = {arXiv:math-ph/0402053},
	number = {1},
	pages = {77--109},
	publisher = {Springer},
	title = {{Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues}},
	volume = {252},
	year = {2004}}

@article{ferrari2003step,
	author = {Ferrari, P. and Spohn, H.},
	date-modified = {2018-02-28 19:41:34 +0000},
	issn = {0022-4715},
	journal = {J. Stat. Phys},
	note = {arXiv:cond-mat/0212456 [cond-mat.stat-mech]},
	number = {1},
	pages = {1--46},
	publisher = {Springer},
	title = {{Step fluctuations for a faceted crystal}},
	volume = {113},
	year = {2003}}

@article{FerrariVeto2013,
	author = {Ferrari, P. and Veto, B.},
	date-added = {2013-10-26 02:11:30 +0000},
	date-modified = {2016-07-05 17:29:13 +0000},
	journal = {Ann. Inst. H. Poincar\'e, Probabilit{\'e}s et Statistiques},
	note = {arXiv:1310.2515 [math.PR]},
	number = {4},
	pages = {1465-1485},
	title = {{Tracy-Widom asymptotics for q-TASEP}},
	volume = {51},
	year = {2015}}

@article{Finkel2007,
	author = {Finkel, J.R. and Grenager, T. and Manning, C.D.},
	booktitle = {ANNUAL MEETING-ASSOCIATION FOR COMPUTATIONAL LINGUISTICS},
	number = {1},
	pages = {272},
	title = {{The infinite tree}},
	volume = {45},
	year = {2007}}

@article{pitman1998additive,
	author = {Fitzsimmons, PJ and Pitman, J.},
	journal = {Stochastic processes and their applications},
	number = {1},
	pages = {117--134},
	publisher = {Citeseer},
	title = {{Kac's moment formula and the Feynman-Kac formula for additive functionals of a Markov process}},
	volume = {79},
	year = {1999}}

@article{FlajoletGuillemin2000BirthDeath,
	author = {Flajolet, P. and Guillemin, F.},
	date-added = {2011-08-03 07:53:19 +0000},
	date-modified = {2011-08-03 07:53:51 +0000},
	title = {The formal theory of birth-and-death processes, lattice path combinatorics and continued fractions},
	year = {2000}}

@article{Fleming1979,
	author = {W. H. Fleming and M. Viot},
	journal = {Indiana Univ. Math. J.},
	owner = {leo},
	pages = {817-843},
	timestamp = {2009.09.20},
	title = {Some measure-valued markov processes in population genetics theory},
	volume = {28},
	year = {1979}}

@article{foda2009hall,
	author = {Foda, O. and Wheeler, M.},
	date-modified = {2018-02-28 19:47:21 +0000},
	issn = {1073-7928},
	journal = {Int. Math. Res. Notices},
	note = {arXiv:0809.2138 [math-ph]},
	number = {14},
	pages = {2597},
	title = {{Hall-Littlewood Plane Partitions and KP}},
	volume = {2009},
	year = {2009}}

@article{fomin1995schensted,
	author = {Fomin, S.},
	journal = {J. Algebr. Comb.},
	number = {1},
	pages = {5--45},
	publisher = {Springer},
	title = {{Schensted algorithms for dual graded graphs}},
	volume = {4},
	year = {1995}}

@article{fomin1995schur,
	author = {Fomin, S.},
	date-modified = {2013-04-28 18:51:50 +0000},
	journal = {Journal of combinatorial theory. Series A},
	number = {2},
	pages = {277--292},
	publisher = {Academic Press},
	title = {{Schur Operators and Knuth Correspondences}},
	volume = {72},
	year = {1995}}

@article{fomin1994duality,
	author = {Fomin, S.},
	journal = {J. Algebr. Comb.},
	number = {4},
	pages = {357--404},
	publisher = {Springer},
	title = {{Duality of graded graphs}},
	volume = {3},
	year = {1994}}

@article{Fomin1986,
    author = {Fomin, S. V.},
    title = {{Generalized Robinson-Schensted-Knuth correspondence}},
    journal = {Journal of Mathematical Sciences},
    volume = {41},
    number = {2},
    pages = {979--991},
    year = {1988},
    doi = {10.1007/BF01247093},
    note = {Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, vol. 155, pp. 156--175, 1986},
}

@mastersthesis{fomin1979thesis,
	author = {Fomin, S.},
	date-added = {2011-09-28 15:23:21 +0000},
	date-modified = {2014-10-30 12:30:05 +0000},
	school = {Leningrad State University},
	title = {{Two-dimensional growth in Dedekind lattices}},
	year = {1979}}

@article{fomin1997rim,
	author = {Fomin, S. and Stanton, D.},
	date-modified = {2011-11-14 16:50:27 +0000},
	journal = {St. Petersburg Mathematical Journal},
	note = {Translated from Algebra i Analiz, {\bf{}9\/} (1997), no. 5, 140--150.},
	number = {5},
	pages = {1007--1016},
	title = {{Rim hook lattices}},
	volume = {9},
	year = {1998}}

@article{FZTP2000,
	author = {Fomin, S. and Zelevinsky, A.},
	date-added = {2012-07-05 08:13:35 +0000},
	date-modified = {2012-09-23 16:03:14 +0000},
	journal = {The Mathematical Intelligencer},
	note = {arXiv:math/9912128 [math.RA]},
	number = {1},
	pages = {23-33},
	title = {{Total positivity: Tests and parametrizations}},
	volume = {22},
	year = {2000}}

@article{fomin1997number,
	author = {Fomin, S. V. and Lulov, N.},
	journal = {Journal of Mathematical Sciences},
	number = {6},
	pages = {4118--4123},
	publisher = {Springer},
	title = {{On the number of rim hook tableaux}},
	volume = {87},
	year = {1997}}

@article{ForrNord2008,
	author = {Forrester, P.J. and Nordenstam, E.},
	date-added = {2012-02-06 14:38:26 +0000},
	date-modified = {2012-02-06 14:39:24 +0000},
	journal = {Moscow Mathematical Journal},
	note = {arXiv:0804.3293 [math.PR]},
	number = {4},
	pages = {749-774},
	title = {{The anti-symmetric GUE minor process}},
	volume = {9},
	year = {2009}}

@article{ForresterRains2007,
	author = {Forrester, P.J. and Rains, E.M.},
	date-added = {2013-04-19 00:50:25 +0000},
	date-modified = {2018-02-28 19:41:34 +0000},
	journal = {J. Stat. Phys},
	note = {arXiv:0705.3925 [math-ph]},
	number = {5-6},
	pages = {833-855},
	title = {{Symmetrized models of last passage percolation and non-intersecting lattice paths}},
	volume = {129},
	year = {2007}}

@article{ForresterRains2005Macdonald,
	author = {Forrester, P.J. and Rains, E.M.},
	date-added = {2014-01-20 19:58:02 +0000},
	date-modified = {2018-02-28 19:38:39 +0000},
	journal = {Probab. Theory Relat. Fields},
	number = {1},
	pages = {1-61},
	title = {{Interpretations of some parameter dependent generalizations of classical matrix ensembles}},
	volume = {131},
	year = {2005}}

@book{Forrester-LogGas,
	author = {Peter J. Forrester},
	owner = {leo},
	publisher = {Princeton University Press},
	timestamp = {2010.08.13},
	title = {{Log-gases and random matrices}},
	year = {2010}}

@article{ForresterWarnaar2007Selberg,
	abstract = {It has been remarked that a fair measure of the impact of Atle Selberg's
	work is the number of mathematical terms which bear his name. One
	of these is the Selberg integral, an n-dimensional generalization
	of the Euler beta integral. We trace its sudden rise to prominence,
	initiated by a question to Selberg from Enrico Bombieri, more than
	thirty years after publication. In quick succession the Selberg integral
	was used to prove an outstanding conjecture in random matrix theory,
	and cases of the Macdonald conjectures. It further initiated the
	study of q-analogues, which in turn enriched the Macdonald conjectures.
	We review these developments and proceed to exhibit the sustained
	prominence of the Selberg integral, evidenced by its central role
	in random matrix theory, Calogero-Sutherland quantum many body systems,
	Knizhnik-Zamolodchikov equations, and multivariable orthogonal polynomial
	theory.},
	author = {Peter J. Forrester and S. Ole Warnaar},
	date-added = {2011-08-04 06:25:59 +0000},
	date-modified = {2011-08-04 06:26:29 +0000},
	eprint = {0710.3981v1},
	note = {arXiv:0710.3981 [math.CA]},
	title = {The importance of the Selberg integral},
	url = {http://arxiv.org/abs/0710.3981v1},
	year = {2007},
	bdsk-url-1 = {http://arxiv.org/abs/0710.3981v1}}

@article{Fortuin1971,
	author = {Fortuin, C.M. and Kasteleyn, P.W. and Ginibre, J.},
	classmath = {{*06D05 (Structure and representation theory of distributive lattices) 62P99 (Appl. of statistics) 62H20 (Statistical measures of associations) }},
	date-modified = {2018-02-28 19:49:00 +0000},
	doi = {10.1007/BF01651330},
	journal = {Comm. Math. Phys},
	language = {English},
	pages = {89-103},
	title = {Correlation inequalities on some partially ordered sets},
	volume = {22},
	year = {1971},
	bdsk-url-1 = {http://dx.doi.org/10.1007/BF01651330}}

@article{Foucart2010,
	author = {Foucart, C.},
	comments = {30 pages},
	eprint = {1006.0581},
	oai2identifier = {1006.0581},
	owner = {leo},
	timestamp = {2010.06.05},
	title = {Distinguished exchangeable coalescents and generalized Fleming-Viot processes with immigration},
	year = {2010}}

@book{fukushima1980dirichlet,
	author = {Fukushima, M.},
	publisher = {Elsevier Science \& Technology},
	title = {{Dirichlet Forms and Markov Processes}},
	year = {1980}}

@conference{fukushima1989skew,
	author = {Fukushima, M. and Oshima, Y.},
	booktitle = {Forum Mathematicum},
	number = {1},
	organization = {Walter de Gruyter, Berlin/New York Berlin, New York},
	pages = {103--142},
	title = {{On the skew product of symmetric diffusion processes}},
	volume = {1},
	year = {1989}}

@article{Fulma2013NT,
	author = {Fulman, J.},
	date-added = {2014-01-19 17:25:23 +0000},
	date-modified = {2015-03-12 12:22:28 +0000},
	journal = {Journal of Group Theory},
	note = {arXiv:1307.0879 [math.NT]},
	number = {4},
	pages = {619--648},
	title = {{Cohen-Lenstra heuristics and random matrix theory over finite fields}},
	volume = {17},
	year = {2014}}

@article{Fulman2007,
	abstract = {It is shown that the combinatorics of commutation relations is well
	suited for analyzing the convergence rate of certain Markov chains.
	Examples studied include random walk on irreducible representations,
	a local random walk on partitions whose stationary distribution is
	the Ewens distribution, and some birth-death chains.},
	author = {Fulman, J.},
	comments = {37 pages; referee suggestions implemented, discuss up-down chains as well, slightly better bounds in Props. 5.6, 7.6},
	date-modified = {2018-02-28 19:38:39 +0000},
	eprint = {0712.1375},
	journal = {Probab. Theory Relat. Fields},
	note = {arXiv:0712.1375 [math.PR]},
	number = {1},
	oai2identifier = {0712.1375},
	owner = {leo},
	pages = {99-136},
	timestamp = {2009.03.25},
	title = {{Commutation relations and Markov chains}},
	url = {http://arxiv.org/abs/0712.1375},
	volume = {144},
	year = {2009},
	bdsk-url-1 = {http://arxiv.org/abs/0712.1375}}

@article{Fulman2009Trees,
	author = {Fulman, J.},
	date-added = {2011-07-15 16:57:10 +0400},
	date-modified = {2018-02-28 19:49:54 +0000},
	journal = {El. Jour. Combin.},
	note = {arXiv:0908.1141 [math.CO]},
	pages = {R139},
	title = {Mixing time for a random walk on rooted trees},
	volume = {16},
	year = {2009}}

@article{Fulman2005,
	author = {Fulman, J.},
	date-modified = {2018-02-28 19:44:38 +0000},
	journal = {Trans. AMS},
	note = {arXiv:math/0305423 [math.RT]},
	number = {2},
	owner = {leo},
	pages = {555-570},
	timestamp = {2009.03.25},
	title = {Stein's method and {P}lancherel measure of the symmetric group},
	url = {http://www.ams.org/tran/2005-357-02/S0002-9947-04-03499-3/home.html},
	volume = {357},
	year = {2005},
	bdsk-url-1 = {http://www.ams.org/tran/2005-357-02/S0002-9947-04-03499-3/home.html}}

@article{Fulman2000RM,
	author = {Fulman, J.},
	date-added = {2014-01-19 17:29:40 +0000},
	date-modified = {2014-01-19 17:30:28 +0000},
	journal = {Bulletin of the American Mathematical Society},
	note = {arXiv:math/0003195 [math.GR]},
	number = {1},
	pages = {51-85},
	title = {{Random matrix theory over finite fields}},
	volume = {39},
	year = {2001}}

@article{Fulman2001,
	abstract = {Connections between longest increasing subsequences in random permutations
	and eigenvalues of random matrices with complex entries have been
	intensely studied. This note applies properties of random elements
	of the finite general linear group to obtain results about the longest
	increasing subsequence in non- uniform random permutations.},
	author = {Jason Fulman},
	comments = {Results for longest decreasing subsequence are added},
	eprint = {math/0109079},
	oai2identifier = {math/0109079},
	owner = {leo},
	timestamp = {2009.04.15},
	title = {${GL(n,q)}$ and Increasing Subsequences in Nonuniform Random Permutations},
	url = {http://arxiv.org/abs/math/0109079},
	year = {2001},
	bdsk-url-1 = {http://arxiv.org/abs/math/0109079}}

@article{Fulman2000eigen,
	author = {Fulman, J.},
	date-added = {2014-01-19 21:17:33 +0000},
	date-modified = {2014-01-19 21:17:58 +0000},
	journal = {Journal of Algebra},
	number = {2},
	pages = {497-511},
	title = {{The Eigenvalue Distribution of a Random Unipotent Matrix in Its Representation on Lines}},
	volume = {228},
	year = {2000}}

@article{Faddeev_Lectures,
	author = {Faddeev, L.D.},
	note = {Les-Houches lectures (1996), arXiv:hep-th/9605187},
	title = {{How algebraic Bethe ansatz works for integrable model}},
	year = {1996}}

@article{Fulman1999,
	author = {Fulman, J.},
	date-added = {2014-01-19 17:33:39 +0000},
	date-modified = {2014-01-19 17:34:04 +0000},
	journal = {Journal of Algebra},
	number = {2},
	pages = {557-590},
	title = {{A probabilistic approach toward conjugacy classes in the finite general linear and unitary groups}},
	volume = {212},
	year = {1999}}

@article{Fulman99New,
	author = {Fulman, J.},
	date-added = {2011-08-01 22:00:08 +0000},
	date-modified = {2011-08-01 22:00:43 +0000},
	note = {arXiv:math/9912148 [math.CO]},
	title = {New Examples of Potential Theory on Bratelli Diagrams},
	year = {1999}}

@article{fulman1997probabilistic,
	author = {Fulman, J.},
	journal = {arxiv preprint},
	note = {arXiv:math/9712237 [math.CO]},
	title = {{Probabilistic measures and algorithms arising from the Macdonald symmetric functions}},
	year = {1997}}

@book{fulton1997young,
	author = {Fulton, W.},
	date-modified = {2013-04-06 22:11:40 +0000},
	isbn = {0521567246},
	publisher = {Cambridge University Press},
	title = {{Young Tableaux with Applications to Representation Theory and Geometry}},
	year = {1997}}

@book{FultonHarris,
	author = {Fulton, W. and Harris, J.},
	date-added = {2012-09-09 16:24:50 +0000},
	date-modified = {2012-09-09 16:25:25 +0000},
	publisher = {Springer},
	title = {{Representation Theory: A First Course}},
	year = {1991}}

@article{Furlinger1985,
	author = {J. Furlinger and J. Hofbauer},
	journal = {Journal of combinatorial theory},
	number = {2},
	owner = {leo},
	pages = {248-264},
	timestamp = {2009.05.11},
	title = {{q-Catalan Numbers}},
	volume = {40},
	year = {1985}}

@article{FerayMeliot2012,
	author = {F{\'e}ray, V. and M{\'e}liot, P-L.},
	date-modified = {2018-04-14 04:20:35 +0000},
	journal = {Probab. Theory Relat. Fields},
	note = {arXiv:1001.2180 [math.RT]},
	number = {3-4},
	owner = {leo},
	pages = {589-624},
	timestamp = {2013.07.21},
	title = {Asymptotics of q-Plancherel measures},
	volume = {152},
	year = {2012}}

@article{ledoux1997talagrand,
	author = {Ledoux, M.},
	date-modified = {2018-12-10 14:09:39 -0500},
	journal = {ESAIM: Probability and statistics},
	pages = {63--87},
	title = {{On Talagrand's deviation inequalities for product measures}},
	volume = {1},
	year = {1997}}

@book{R.GangolliV.S.Varadarajan.,
	author = {Gangolli, R. and Varadarajan, V.S.},
	date-added = {2013-09-21 17:45:42 +0000},
	date-modified = {2013-09-21 17:46:32 +0000},
	journal = {Ergebnisse der Mathematik},
	publisher = {Springer Verlag},
	title = {{Harmonic analysis of spherical functions on real reductive spaces}},
	volume = {101},
	year = {1988}}

@book{GantmacherKrein1950,
	author = {Gantmacher, F.R. and Krein, M.G.},
	date-added = {2012-11-02 14:35:56 +0000},
	date-modified = {2012-11-02 14:39:05 +0000},
	publisher = {AMS Chelsea Publishing},
	title = {Oscillation matrices and kernels and small vibrations of mechanical systems},
	year = {2002}}

@article{Garsia1972,
	address = {Berkeley, Calif.},
	author = {Adriano Garsia},
	booktitle = {Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. II: Probability theory},
	mrclass = {60G15},
	mrnumber = {53 \#14623},
	mrreviewer = {P. Laurie Davies},
	pages = {369-374},
	publisher = {Univ. California Press},
	title = {Continuity properties of {G}aussian processes with multidimensional time parameter},
	year = {1972}}

@book{GasperRahman,
	author = {Gasper, G. and Rahman, M.},
	date-added = {2013-10-13 20:19:47 +0000},
	date-modified = {2013-10-13 20:20:23 +0000},
	publisher = {Cambridge University Press},
	title = {{Basic hypergeometric series}},
	year = {2004}}

@article{Gekhtman2011Pentagram,
	abstract = {The pentagram map that associates to a projective polygon a new one
	formed by intersections of short diagonals was introduced by R. Schwartz
	and was shown to be integrable by V. Ovsienko, R. Schwartz and S.
	Tabachnikov. Recently, M. Glick demonstrated that the pentagram map
	can be put into the framework of the theory of cluster algebras.},
	author = {Gekhtman, M. and Shapiro, M. and Tabachnikov, S. and Vainshtein, A.},
	date-added = {2012-09-23 12:30:49 +0000},
	date-modified = {2012-09-23 12:31:25 +0000},
	title = {{Higher pentagram maps, weighted directed networks, and cluster dynamics}},
	year = {2011},
	bdsk-url-1 = {http://arxiv.org/abs/1110.0472}}

@article{GerasimovLebedevOblezin2011,
	author = {Gerasimov, A. and Lebedev, D. and Oblezin, S.},
	date-added = {2013-01-12 23:50:51 +0000},
	date-modified = {2020-03-20 18:16:16 -0400},
	journal = {{Letters in Mathematical Physics}},
	note = {arXiv:1101.4567 [math.AG]},
	number = {3},
	pages = {279-290},
	title = {{On a classical limit of $q$-deformed Whittaker functions}},
	volume = {100},
	year = {2012}}

@article{gessel1985binomial,
	author = {Gessel, I. and Viennot, G.},
	date-added = {2012-11-04 22:01:54 +0000},
	date-modified = {2012-11-04 22:01:54 +0000},
	journal = {Adv. Math.},
	number = {3},
	pages = {300--321},
	publisher = {Elsevier},
	title = {Binomial determinants, paths, and hook length formulae},
	volume = {58},
	year = {1985}}

@article{GesselXin2004qDyson,
	abstract = {We give a formal Laurent series proof of Andrews's $q$-Dyson Conjecture,
	first proved by Zeilberger and Bressoud.},
	author = {Ira M. Gessel and Guoce Xin},
	date-added = {2011-08-04 06:27:45 +0000},
	date-modified = {2011-08-04 06:28:12 +0000},
	eprint = {math/0412339v2},
	note = {arXiv:math/0412339 [math.CO]},
	title = {A Short Proof of the Zeilberger-Bressoud $q$-Dyson Theorem},
	url = {http://arxiv.org/abs/math/0412339v2},
	bdsk-url-1 = {http://arxiv.org/abs/math/0412339v2}}

@article{Ghahramani2005,
	author = {Ghahramani, Z.},
	booktitle = {Tutorial presentation at the UAI Conference},
	organization = {Citeseer},
	title = {{Non-parametric bayesian methods}},
	year = {2005}}

@book{Ghosh2003,
	author = {Ghosh, J.K. and Ramamoorthi, R.V.},
	owner = {leo},
	publisher = {Springer-Verlag},
	timestamp = {2010.01.12},
	title = {{Bayesian Nonparametrics}},
	year = {2003}}

@book{gikhman2004theoryII,
	author = {Gikhman, I.I. and Skorokhod, A.V. and Kotz, S.},
	publisher = {Springer Verlag},
	title = {{The theory of stochastic processes II}},
	year = {2004}}

@article{Gnedin2009a,
	abstract = {A one-parameter family of exchangeable partitions with a simple updating
	rule is introduced. The partition is identified with a randomized
	version of a standard symmetric species-sampling model with finitely
	many types.},
	author = {Gnedin, A.},
	date-modified = {2018-02-28 19:49:16 +0000},
	eprint = {0910.1988},
	journal = {Electron. Commun. Probab.},
	note = {arXiv:0910.1988 [math.PR]},
	oai2identifier = {0910.1988},
	owner = {leo},
	pages = {79--88},
	timestamp = {2009.10.14},
	title = {A Species Sampling Model with Finitely many Types},
	volume = {15},
	year = {2010}}

@article{Gnedin2009Boundaries,
	author = {Gnedin, A.},
	date-added = {2011-07-15 15:54:48 +0400},
	date-modified = {2011-07-15 15:55:40 +0400},
	note = {arXiv:0909.4933 [math.PR]},
	title = {Boundaries from inhomogeneous Bernoulli trials},
	year = {2009}}

@unpublished{Gnedin-ex-part,
	author = {Alexander Gnedin},
	note = {Unpublished paper},
	owner = {leo},
	timestamp = {2009.03.11},
	title = {Exchangeable partitions and symmetric functions},
	year = {2005}}

@article{gnedin2004three,
	author = {Gnedin, A.},
	journal = {Combinatorics, Probability and Computing},
	note = {arXiv:math/0210319 [math.PR]},
	number = {02},
	pages = {185--193},
	publisher = {Cambridge Univ Press},
	title = {{Three sampling formulas}},
	volume = {13},
	year = {2004}}

@article{Gnedin1997,
	author = {Alexander Gnedin},
	journal = {Ann. Probab.},
	number = {3},
	owner = {leo},
	pages = {1437--1450},
	timestamp = {2009.03.11},
	title = {The representation of composition structures},
	volume = {25},
	year = {1997}}

@article{GnedinOlsh2009q,
	author = {Gnedin, A. and Olshanski, G.},
	date-added = {2011-07-15 15:58:25 +0400},
	date-modified = {2016-05-04 16:38:43 +0000},
	journal = {{Ann. Probab.}},
	note = {arXiv:0907.3275 [math.PR]},
	number = {6},
	pages = {2103--2135},
	title = {q-Exchangeability via quasi-invariance},
	volume = {38},
	year = {2010}}

@article{Gnedin2009,
	abstract = {A q-analogue of de Finetti's theorem is obtained in terms of a boundary
	problem for the q-Pascal graph. For q a power of prime this leads
	to a characterisation of random spaces over the Galois field F_q
	that are invariant under the natural action of the infinite group
	of invertible matrices with coefficients from F_q.},
	author = {Gnedin, A. and Olshanski, G.},
	comments = {LaTeX, 15 pages},
	date-modified = {2018-09-27 22:29:35 -0400},
	eprint = {0905.0367},
	journal = {El. Jour. Combin.},
	note = {arXiv:0905.0367 [math.PR]},
	oai2identifier = {0905.0367},
	owner = {leo},
	pages = {R16},
	timestamp = {2009.05.08},
	title = {A q-analogue of de {F}inetti's theorem},
	volume = {16},
	year = {2009},
	bdsk-url-1 = {http://arxiv.org/abs/0905.0367}}

@article{GnedinIntern.Math.ResearchNotices2006Art.ID5196839pp.,
	abstract = {The graph of zigzag diagrams is a close relative of Young's lattice.
	The boundary problem for this graph amounts to describing coherent
	random permutations with descent-set statistic, and is also related
	to certain positive characters on the algebra of quasi-symmetric
	functions. We establish connections to some further relatives of
	Young's lattice and solve the boundary problem by reducing it to
	the classification of spreadable total orders on integers, as recently
	obtained by Jacka and Warren.},
	author = {Alexander Gnedin and Grigori Olshanski},
	comments = {Version 2: more detailed exposition, 4 references added, page format changed, 44 pp.; accepted in IMRN},
	date-modified = {2018-02-28 19:47:33 +0000},
	eprint = {math/0508131},
	journal = {Int. Math. Res. Notices},
	note = {arXiv:math/0508131v2 [math.CO]},
	oai2identifier = {math/0508131},
	owner = {leo},
	pages = {Art. ID 51968, 39pp.},
	timestamp = {2009.03.11},
	title = {Coherent permutations with descent statistic and the boundary problem for the graph of zigzag diagrams},
	url = {http://arxiv.org/abs/math/0508131},
	year = {2006},
	bdsk-url-1 = {http://arxiv.org/abs/math/0508131}}

@article{GnedinOlsh2006,
	author = {Gnedin, A. and Olshanski, G.},
	date-added = {2012-09-10 11:42:15 +0000},
	date-modified = {2012-09-10 11:44:29 +0000},
	journal = {Moscow Mathematical Journal},
	note = {arXiv:math/0602610},
	number = {3},
	pages = {461-475},
	title = {{The boundary of Eulerian number triangle}},
	volume = {6},
	year = {2006}}

@article{Gnedin2005,
	abstract = {A new class of random composition structures (the ordered analog of
	Kingman's partition structures) is defined by a regenerative description
	of component sizes. Each regenerative composition structure is represented
	by a process of random sampling of points from an exponential distribution
	on the positive halfline, and separating the points into clusters
	by an independent regenerative random set. Examples are composition
	structures derived from residual allocation models, including one
	associated with the Ewens sampling formula, and composition structures
	derived from the zero set of a Brownian motion or Bessel process.
	We provide characterisation results and formulas relating the distribution
	of the regenerative composition to the L{\'e}vy parameters of a subordinator
	whose range is the corresponding regenerative set. In particular,
	the only reversible regenerative composition structures are those
	associated with the interval partition of $[0,1]$ generated by excursions
	of a standard Bessel bridge of dimension $2 - 2 \alpha$ for some
	$\alpha \in [0,1]$.},
	author = {Alexander Gnedin and Jim Pitman},
	eprint = {math/0307307},
	journal = {Ann. Probab.},
	number = {2},
	oai2identifier = {math/0307307},
	owner = {leo},
	pages = {445-479},
	timestamp = {2009.03.12},
	title = {Regenerative Composition Structures},
	url = {http://arxiv.org/abs/math/0307307},
	volume = {33},
	year = {2005},
	bdsk-url-1 = {http://arxiv.org/abs/math/0307307}}

@article{Gnedin2005a,
	abstract = {We consider Kingman's partition structures which are regenerative
	with respect to a general operation of random deletion of some part.
	Prototypes of this class are the Ewens partition structures which
	Kingman characterised by regeneration after deletion of a part chosen
	by size-biased sampling. We associate each regenerative partition
	structure with a corresponding regenerative composition structure,
	which (as we showed in a previous paper) can be associated in turn
	with a regenerative random subset of the positive halfline, that
	is the closed range of a subordinator. A general regenerative partition
	structure is thus represented in terms of the Laplace exponent of
	an associated subordinator. We also analyse deletion properties characteristic
	of the two-parameter family of partition structures.},
	author = {Alexander Gnedin and Jim Pitman},
	date-modified = {2018-02-28 19:49:54 +0000},
	eprint = {math/0408071},
	journal = {El. Jour. Combin.},
	oai2identifier = {math/0408071},
	owner = {leo},
	pages = {R12},
	timestamp = {2009.03.12},
	title = {Regenerative partition structures},
	url = {http://arxiv.org/abs/math/0408071},
	volume = {11 (2)},
	year = {2005},
	bdsk-url-1 = {http://arxiv.org/abs/math/0408071}}

@article{GnedinPitman2005,
	author = {Gnedin, A. and Pitman, J.},
	date-added = {2012-09-10 11:40:31 +0000},
	date-modified = {2012-09-10 11:41:32 +0000},
	journal = {Zapiski Nauchn. Semin. POMI},
	note = {reproduced in J. Math. Sci., New York 138 (2006), No. 3, 5674--5685; arXiv:math/0412494.},
	pages = {83-102},
	title = {{Exchangeable Gibbs partitions and Stirling triangles}},
	volume = {325},
	year = {2005}}

@phdthesis{Goldwater2007,
	author = {Goldwater, S.J.},
	school = {Citeseer},
	title = {{Nonparametric Bayesian models of lexical acquisition}},
	year = {2007}}

@article{Goldwater2006,
	author = {Goldwater, S. and Griffiths, T. and Johnson, M.},
	journal = {Advances in Neural Information Processing Systems},
	pages = {459},
	publisher = {Citeseer},
	title = {{Interpolating between types and tokens by estimating power-law generators}},
	volume = {18},
	year = {2006}}

@article{GoncharovKenyon2011DimersClusterIntSys,
	author = {Goncharov, A.B. and Kenyon, R.},
	date-added = {2011-08-03 08:15:01 +0000},
	date-modified = {2011-08-03 08:15:51 +0000},
	note = {arXiv:1107.5588 [math.AG]},
	title = {Dimers and cluster integrable systems},
	year = {2011}}

@article{Goncharov1944,
	author = {Goncharov, VL},
	journal = {Izvestia Akad. Nauk. SSSR, Ser. Mat},
	pages = {3--48},
	title = {{Some facts from combinatorics}},
	volume = {8},
	year = {1944}}

@article{KerovGoodman1997,
	abstract = {We find the Martin boundary for the Young-Fibonacci lattice YF. Along
	with the lattice of Young diagrams, this is the most interesting
	example of a differential poset. The Martin boundary construction
	provides an explicit Poisson-type integral representation of non-negative
	harmonic functions on YF. The latter are in a canonical correspondence
	with a set of traces on Okada locally semisimple algebra. The set
	is known to contain all the indecomposable traces. Presumably, all
	of the traces in the set are indecomposable, though we have no proof
	of this conjecture. Using a new explicit product formula for Okada
	characters, we derive precise regularity conditions under which a
	sequence of characters of finite-dimensional Okada algebras converges
	to a character of the infinite-dimensional one.},
	author = {F.M. Goodman and S.V. Kerov},
	comments = {30 pages, AmSTeX, uses EPSF, one EPS figure},
	eprint = {math/9712266},
	oai2identifier = {math/9712266},
	owner = {leo},
	timestamp = {2010.07.15},
	title = {The Martin Boundary of the Young-Fibonacci Lattice},
	year = {1997}}

@article{Gorin2010q,
	author = {Gorin, V.},
	date-added = {2011-12-03 14:19:42 +0000},
	date-modified = {2012-06-25 08:31:46 +0000},
	journal = {Adv. Math.},
	note = {arXiv:1011.1769 [math.RT]},
	number = {1},
	pages = {201-266},
	title = {{The q-Gelfand-Tsetlin graph, Gibbs measures and q-Toeplitz matrices}},
	volume = {229},
	year = {2012}}

@article{Gorin2008Jacobi,
	author = {Gorin, V.},
	journal = {Journal of Mathematical Sciences},
	note = {arXiv:0812.3146 [math.PR]},
	number = {6},
	pages = {819--837},
	publisher = {Springer},
	title = {{Noncolliding Jacobi processes as limits of Markov chains on the Gelfand--Tsetlin graph}},
	volume = {158},
	year = {2009}}

@article{Gorin2008Jacobi_eng,
	author = {Gorin, V.},
	journal = {Journal of Mathematical Sciences},
	note = {arXiv:0812.3146 [math.PR]},
	number = {6},
	owner = {leo},
	pages = {819--837},
	publisher = {Springer},
	timestamp = {2010.10.29},
	title = {{Noncolliding Jacobi processes as limits of Markov chains on the Gelfand--Tsetlin graph}},
	volume = {158},
	year = {2009}}

@article{Gorin2007Hexagon,
	author = {Gorin, V.},
	date-added = {2012-01-13 21:36:09 +0000},
	date-modified = {2012-02-03 00:28:13 +0000},
	journal = {Funct. Anal. Appl.},
	note = {arXiv:0708.2349 [math.PR]},
	number = {3},
	pages = {180-197},
	title = {Nonintersecting paths and the {H}ahn orthogonal polynomial ensemble},
	volume = {42},
	year = {2008},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=2454474}}

@article{GorinKerovVershikFq2012,
	author = {Gorin, V. and Kerov, S. and Vershik, A.},
	date-modified = {2014-02-22 01:04:02 +0000},
	journal = {Adv. Math.},
	note = {arXiv:1209.4945 [math.RT]},
	owner = {leo},
	pages = {331-395},
	timestamp = {2013.07.21},
	title = {Finite traces and representations of the group of infinite matrices over a finite field},
	volume = {254},
	year = {2014}}

@article{GorinPanova2012,
	author = {Gorin, V. and Panova, G.},
	date-added = {2012-07-06 08:08:21 +0000},
	date-modified = {2015-03-20 19:27:45 +0000},
	journal = {DMTCS Proceedings, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)},
	note = {arXiv:1301.0634 [math.RT]},
	pages = {37--48},
	title = {{Asymptotics of symmetric polynomials with applications to statistical mechanics and representation theory. Extended abstract}},
	year = {2013}}

@article{gorsky2015refined,
	author = {Gorsky, E. and Negu{\c{t}}, A.},
	journal = {Journal de Math{\'e}matiques Pures et Appliqu{\'e}es},
	note = {arXiv:1304.3328 [math.RT]},
	number = {3},
	pages = {403--435},
	title = {Refined knot invariants and Hilbert schemes},
	volume = {104},
	year = {2015}}

@article{Gorsky2010,
	abstract = {We propose an algebraic model of the conjectural triply graded homology
	of Gukov, Dunfield and Rasmussen for some torus knots. It turns out
	to be related to the q,t-Catalan numbers of Garsia and Haiman.},
	author = {E. Gorsky},
	comments = {The main combinatorial statement is weakened to the case n<5},
	eprint = {1003.0916},
	oai2identifier = {1003.0916},
	owner = {leo},
	timestamp = {2010.06.05},
	title = {q,t-Catalan numbers and knot homology},
	year = {2010}}

@article{Gough2003BosonFermion,
	author = {Gough, J.},
	date-added = {2011-08-03 07:56:07 +0000},
	date-modified = {2011-08-03 07:56:39 +0000},
	note = {arXiv:math-ph/0309024},
	title = {Boson-Fermion unification implemented by Wick calculus},
	year = {2003}}

@article{Gould1960,
	author = {Gould, H. W.},
	date-added = {2011-12-19 15:17:47 +0000},
	date-modified = {2014-10-25 19:09:00 +0000},
	fjournal = {Duke Mathematical Journal},
	journal = {Duke J. Math.},
	pages = {281--289},
	title = {The {$q$}-{S}tirling numbers of first and second kinds},
	volume = {28},
	year = {1961},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=0122759}}

@book{goulden2004combinatorial,
	author = {Goulden, I.P. and Jackson, D.M.},
	isbn = {0486435970},
	publisher = {Dover Pubns},
	title = {{Combinatorial enumeration}},
	year = {2004}}

@conference{grabiner1999brownian,
	author = {Grabiner, D.J.},
	booktitle = {Annales de l'Institut Henri Poincare (B) Probability and Statistics},
	number = {2},
	organization = {Elsevier},
	pages = {177--204},
	title = {{Brownian motion in a Weyl chamber, non-colliding particles, and random matrices* 1}},
	volume = {35},
	year = {1999}}

@book{graham1994concrete,
	author = {Graham, R.L. and Knuth, D.E. and Patashnik, O.},
	publisher = {Addison-Wesley Reading, MA},
	title = {{Concrete mathematics: a foundation for computer science}},
	year = {1994}}

@article{Greene1974,
	author = {Greene, C.},
	date-added = {2013-10-13 15:45:56 +0000},
	date-modified = {2013-10-13 15:46:27 +0000},
	journal = {Adv. Math.},
	number = {2},
	pages = {254--265},
	title = {{An extension of Schensted's theorem}},
	volume = {14},
	year = {1974}}

@article{Grenander1976,
	author = {Grenander, U.},
	title = {{Lectures in pattern theory-Volume 1: Pattern synthesis}},
	year = {1976}}

@article{GuilleminSternberg1982,
	author = {Guillemin, V. and Sternberg, S.},
	date-added = {2013-10-15 23:40:07 +0000},
	date-modified = {2013-10-15 23:42:26 +0000},
	journal = {Invent. Math.},
	number = {3},
	pages = {515--538},
	title = {{Geometric quantization and multiplicities of group representations}},
	volume = {67},
	year = {1982}}

@article{Hahn1949,
	author = {Hahn, W.},
	date-added = {2012-09-17 02:06:44 +0000},
	date-modified = {2012-09-17 02:07:27 +0000},
	journal = {Mathematische Nachrichten},
	pages = {340--379},
	title = {{Beitraege zur Theorie der Heineschen Reihen. Die 24 Integrale der hyper- geometrischen q-Differenzengleichung. Das q-Analogon der Laplace-Transformation}},
	volume = {2},
	year = {1949}}

@article{Haiman2004,
	author = {Mark Haiman and Alexander Woo},
	owner = {leo},
	timestamp = {2009.05.11},
	title = {Geometry of q and q, t-{A}nalogs in {C}ombinatorial {E}numeration},
	year = {2004}}

@book{Hamermesh1962,
	author = {Hamermesh, M.},
	date-added = {2011-06-17 14:35:52 +0400},
	date-modified = {2011-06-17 14:36:37 +0400},
	publisher = {Addison-Wesley Reading, MA},
	title = {Group theory and its application to physical problems},
	year = {1962}}

@incollection{hammersley1972few,
	author = {Hammersley, J.M.},
	booktitle = {{Proc. Sixth Berkeley Symp. Math. Statist. and Probability}},
	pages = {345--394},
	title = {{A few seedlings of research}},
	volume = {1},
	year = {1972}}

@article{Handa2007,
	abstract = {The two-parameter Poisson-Dirichlet distribution is a probability
	distribution on the totality of positive decreasing sequences with
	sum 1 and hence considered to govern masses of a random discrete
	distribution. A characterization of the associated point process
	(i.e., the random point process obtained by regarding the masses
	as points in the positive real line) is given in terms of the correlation
	functions. Relying on this, we apply the theory of point processes
	to reveal mathematical structure of the two-parameter Poisson-Dirichlet
	distribution. Also, developing the Laplace transform approach due
	to Pitman and Yor, we will be able to extend several results previously
	known for the one-parameter case, and the Markov-Krein identity for
	the generalized Dirichlet process is discussed from a point of view
	of functional analysis based on the two-parameter Poisson-Dirichlet
	distribution.},
	author = {Handa, K.},
	comments = {52 pages, LaTeX; the former Theorem 6.1 (ii) removed, a unified labeling for results, added references},
	eprint = {0705.3496},
	journal = {Bernoulli},
	oai2identifier = {0705.3496},
	owner = {leo},
	pages = {1082-1116},
	timestamp = {2009.08.12},
	title = {{The two-parameter Poisson-Dirichlet point process}},
	volume = {15},
	year = {2009}}

@book{Hardy1956,
	author = {G. H. Hardy and E. M. Wright},
	owner = {leo},
	publisher = {Oxford Univ. Press},
	timestamp = {2009.07.26},
	title = {{An Introduction to the Theory of Numbers}},
	year = {1956}}

@article{hawkes1973measure,
	author = {Hawkes, J.},
	journal = {Bull. London Math. Soc},
	pages = {21--28},
	title = {{The measure of the range of a subordinator}},
	volume = {5},
	year = {1973}}

@article{gerasimov2008baxter,
	author = {Gerasimov, A. and Lebedev, D. and Oblezin, S.},
	journal = {Commun. Math. Phys.},
	note = {arXiv:0706.3476 [math.RT]},
	number = {3},
	pages = {867},
	publisher = {Springer},
	title = {Baxter operator and Archimedean Hecke algebra},
	volume = {284},
	year = {2008}}

@article{Hazewinkel2004,
	abstract = {In [5, 6] it has been proved that the ring of quasisymmetric functions
	over the integers is free polynomial, see also [4]. This is a matter
	that has been of great interest since 1972; for instance because
	of the role this statement plays in a classification theory for noncommutative
	formal groups that has been in development since then, see [2] and
	[9] and the references in the latter. Meanwhile quasisymmetric functions
	have found many more applications, [3]. However, the proofs in [5,
	6] do not give explicit polynomial generators for QSymm over the
	integers. In this note I give a (really quite simple) set of polynomial
	generators for QSymm over the integers.},
	author = {Michiel Hazewinkel},
	comments = {7 pages. Submitted to CR Acad. Sci. Paris},
	eprint = {math/0410366},
	oai2identifier = {math/0410366},
	owner = {leo},
	timestamp = {2009.03.16},
	title = {Explicit polynomial generators for the ring of quasi-symmetric functions over the integers},
	url = {http://arxiv.org/abs/math/0410366},
	year = {2004},
	bdsk-url-1 = {http://arxiv.org/abs/math/0410366}}

@article{Heckmann1982,
	author = {Heckmann, G.J.},
	date-added = {2013-10-15 23:39:30 +0000},
	date-modified = {2013-10-15 23:40:03 +0000},
	journal = {Invent. Math.},
	number = {2},
	pages = {333--356},
	title = {{Projections of orbits and asymptotic behavior of multiplicities for compact connected Lie groups}},
	volume = {67},
	year = {1982}}

@article{HeckmannOpdam1997,
	author = {Heckmann, G.J. and Opdam, E.M.},
	date-added = {2013-09-07 12:39:55 +0000},
	date-modified = {2013-09-07 12:40:36 +0000},
	journal = {Ann. Math.},
	number = {1},
	pages = {139--173},
	title = {{Yang's system of particles and Hecke algebras}},
	volume = {145},
	year = {1997}}

@book{HelBook,
	address = {London},
	author = {Helgason, S.},
	date-added = {2013-09-21 17:45:11 +0000},
	date-modified = {2013-09-21 17:45:36 +0000},
	publisher = {Academic press},
	title = {{Groups and geometric analysis}},
	year = {1984}}

@article{Helgason66,
	author = {Helgason, S.},
	date-added = {2013-09-21 17:44:42 +0000},
	date-modified = {2013-09-21 17:45:05 +0000},
	journal = {Math. Ann.},
	pages = {297-308},
	title = {{An analogue of the Paley-Wiener theorem for the Fourier transform on certain symmetric spaces}},
	volume = {165},
	year = {1966}}

@article{Hoffman2003TreesHopf,
	author = {Hoffman, M.E.},
	coden = {TAMTAM},
	date-added = {2011-11-14 16:52:44 +0000},
	date-modified = {2018-02-28 19:44:38 +0000},
	doi = {10.1090/S0002-9947-03-03317-8},
	fjournal = {Transactions of the American Mathematical Society},
	issn = {0002-9947},
	journal = {Trans. AMS},
	note = {arXiv:math/0201253 [math.CO]},
	number = {9},
	pages = {3795--3811 (electronic)},
	title = {Combinatorics of rooted trees and {H}opf algebras},
	url = {http://dx.doi.org/10.1090/S0002-9947-03-03317-8},
	volume = {355},
	year = {2003},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=1990174},
	bdsk-url-2 = {http://dx.doi.org/10.1090/S0002-9947-03-03317-8}}

@book{Hoffman1992,
	author = {Hoffman, P.N. and Humphreys, J.F.},
	owner = {leo},
	publisher = {Oxford Univ. Press},
	timestamp = {2009.03.26},
	title = {Projective representations of the symmetric groups},
	year = {1992}}

@article{Hofmann1999,
	author = {Hofmann, T.},
	booktitle = {Proceedings of the 22nd annual international ACM SIGIR conference on Research and development in information retrieval},
	organization = {ACM New York, NY, USA},
	pages = {50--57},
	title = {{Probabilistic latent semantic indexing}},
	year = {1999}}

@article{Hollander2006,
	abstract = {. In this paper we give a survey of some recent results for random
	walk in random scenery (RWRS). On $\mathbb {Z}^d$, $d\geq 1$, we
	are given a random walk with i.i.d. increments and a random scenery
	with i.i.d. components. The walk and the scenery are assumed to be
	independent. RWRS is the random process where time is indexed by
	$\mathbb {Z}$, and at each unit of time both the step taken by the
	walk and the scenery value at the site that is visited are registered.
	We collect various results that classify the ergodic behavior of
	RWRS in terms of the characteristics of the underlying random walk
	(and discuss extensions to stationary walk increments and stationary
	scenery components as well). We describe a number of results for
	scenery reconstruction and close by listing some open questions.},
	author = {Frank den Hollander and Jeffrey E. Steif},
	comments = {Published at http://dx.doi.org/10.1214/074921706000000077 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)},
	eprint = {math/0608219},
	journal = {IMS Lecture Notes--Monograph Series},
	oai2identifier = {math/0608219},
	owner = {leo},
	pages = {53-65},
	reportno = {IMS-LNMS48-LNMS4806},
	timestamp = {2009.04.03},
	title = {Random walk in random scenery: A survey of some recent results},
	url = {http://arxiv.org/abs/math/0608219},
	volume = {48},
	year = {2006},
	bdsk-url-1 = {http://arxiv.org/abs/math/0608219}}

@article{holst2001poisson,
	author = {Holst, L.},
	date-modified = {2014-01-03 12:32:38 +0000},
	journal = {Preprint of the Royal Institute of Technology, Stockholm, Sweden},
	publisher = {Citeseer},
	title = {{The Poisson--Dirichlet distribution and its relatives revisited}},
	year = {2001}}

@article{horowitz1968hausdorff,
	author = {Horowitz, J.},
	journal = {Israel Journal of Mathematics},
	number = {2},
	pages = {176--182},
	publisher = {Springer},
	title = {{The Hausdorff dimension of the sample path of a subordinator}},
	volume = {6},
	year = {1968}}

@article{Houdre2006,
	author = {Christian Houdre and Trevis J. Litherland},
	owner = {leo},
	timestamp = {2010.01.09},
	title = {{On the Longest Increasing Subsequence for Finite and Countable Alphabets}},
	year = {2006}}

@article{peres2006determinantal,
	author = {Hough, J.B. and Krishnapur, M. and Peres, Y. and Vir{\'a}g, B.},
	journal = {Probability Surveys},
	note = {arXiv:math/0503110 [math.PR]},
	pages = {206--229},
	title = {{Determinantal processes and independence}},
	volume = {3},
	year = {2006}}

@article{Ignatov1982,
	author = {Ignatov, T.},
	journal = {THEORY PROB. \& APPLIC.},
	number = {1},
	pages = {136--147},
	title = {{Constant arising in the asymptotic theory of symmetric groups, and on Poisson-Dirichlet measures.}},
	volume = {27},
	year = {1982}}

@article{ishikawa2010q,
	author = {Ishikawa, M. and Tagawa, H. and Zeng, J.},
	date-added = {2012-11-05 02:11:58 +0000},
	date-modified = {2012-11-05 02:12:28 +0000},
	note = {arXiv:1009.2004 [math.CO]},
	title = {A q-analogue of Catalan Hankel determinants},
	year = {2010}}

@article{Ishwaran2003,
	author = {Ishwaran, H. and James, L.F.},
	journal = {Statistica Sinica},
	number = {4},
	pages = {1211--1236},
	publisher = {Citeseer},
	title = {{Generalized weighted Chinese restaurant processes for species sampling mixture models}},
	volume = {13},
	year = {2003}}

@article{Ishwaran2003a,
	author = {Ishwaran, H. and Zarepour, M.},
	journal = {Arxiv preprint math/0309041},
	title = {{Random probability measures via Polya sequences: revisiting the Blackwell-MacQueen urn scheme}},
	year = {2003}}

@article{Ismagilov1970,
	author = {Ismagilov, R.S.},
	date-added = {2011-06-16 12:48:45 +0400},
	date-modified = {2011-06-16 12:53:58 +0400},
	journal = {Funktsional. Anal. i Prilozhen.},
	number = {1},
	pages = {42-51},
	title = {Spherical functions over a valuated field with an infinite residue field},
	volume = {4},
	year = {1970}}

@article{Ismagilov1969,
	author = {Ismagilov, R.S.},
	date-added = {2011-06-16 12:47:35 +0400},
	date-modified = {2011-06-16 12:48:42 +0400},
	journal = {Izvestia Akad. Nauk. SSSR, Ser. Mat},
	number = {6},
	pages = {1296-1323},
	title = {On linear representations of groups of matrices with elements from a valuated field},
	volume = {33},
	year = {1969}}

@article{its1990differential,
	author = {Its, A.R. and Izergin, A.G. and Korepin, V.E. and Slavnov, N.A.},
	journal = {Int. J. Mod. Phys. B},
	number = {5},
	pages = {1003--1037},
	title = {{Differential equations for quantum correlation functions}},
	volume = {4},
	year = {1990}}

@article{Ivancevic2008DeRhamHodge,
	author = {Ivancevic, V.G. and Ivancevic, T.T.},
	date-added = {2011-08-03 07:14:59 +0000},
	date-modified = {2011-08-03 07:15:59 +0000},
	note = {arXiv:0807.4991 [math.DG]},
	title = {Undergraduate Lecture Notes in De Rham-Hodge Theory}}

@incollection{ivanov2006plancherel,
	author = {Ivanov, V.},
	booktitle = {Representation theory, dynamical systems, and asymptotic combinatorics},
	journal = {Representation theory, dynamical systems, and asymptotic combinatorics},
	pages = {73-86},
	publisher = {Transl. AMS},
	series = {2},
	title = {{Plancherel measure on shifted Young diagrams}},
	volume = {217},
	year = {2006}}

@article{ivanov2004gaussian,
	author = {Ivanov, VN},
	issn = {1072-3374},
	journal = {Journal of Mathematical Sciences},
	number = {3},
	pages = {2330--2344},
	publisher = {Springer},
	title = {{Gaussian limit for projective characters of large symmetric groups}},
	volume = {121},
	year = {2004}}

@article{IvanovNewYork3517-3530,
	abstract = {Classical Schur P-functions are the particular case of Hall-Littlewood
	polynomials when the parameter is equal to -1. We introduce factorial
	(interpolation) analogues of Schur P-functions. A dimension of a
	skew shifted Young diagram is the number of standard tableaux of
	the given shape. Also these numbers are equal up to simple factors
	to the decomposition coefficients of the restriction of an irreducible
	representation of a spin-symmetric group to a smaller spin-symmetric
	group. In terms of the factorial Schur P-functions we obtain an explicit
	formula for the dimension of a skew shifted Young diagram. The main
	application of this formula is the new derivation of Nazarov's classification
	of undecomposable projective characters of the infinite symmetric
	group.},
	author = {Ivanov, V.},
	comments = {AMS-TeX, 16 pages, 2 figures},
	eprint = {math/0303169},
	journal = {Jour. Math. Sci. (New York)},
	note = {in Russian: Zap. Nauchn. Sem. POMI {\bf{}240\/} (1997), 115-135, arXiv:math/0303169 [math.CO]},
	number = {5},
	oai2identifier = {math/0303169},
	owner = {leo},
	pages = {3517-3530},
	timestamp = {2009.03.11},
	title = {The {D}imension of {S}kew {S}hifted {Y}oung {D}iagrams, and {P}rojective {C}haracters of the {I}nfinite {S}ymmetric {G}roup},
	url = {http://arxiv.org/abs/math/0303169},
	volume = {96},
	year = {1999},
	bdsk-url-1 = {http://arxiv.org/abs/math/0303169}}

@article{ivanov2002kerov,
	author = {Ivanov, V. and Olshanski, G.},
	journal = {Symmetric Functions 2001: Surveys of developments and perspectives},
	note = {arXiv:math/0304010 [math.CO]},
	title = {{Kerov's central limit theorem for the Plancherel measure on Young diagrams}},
	year = {2002}}

@article{Jack2,
	author = {Jack, H.},
	date-added = {2013-08-15 19:05:29 +0000},
	date-modified = {2013-08-15 19:06:53 +0000},
	journal = {Proc. R. Soc. Edinburgh A},
	pages = {347-363},
	title = {A surface integral and symmetric functions},
	volume = {69},
	year = {1972}}

@article{Jack1,
	author = {Jack, H.},
	date-added = {2013-08-15 19:04:21 +0000},
	date-modified = {2013-08-15 19:05:47 +0000},
	journal = {Proc. R. Soc. Edinburgh A},
	number = {1-18},
	title = {A class of symmetric functions with a parameter},
	volume = {69},
	year = {1970}}

@article{Jacka2005,
	abstract = {In this paper we study random orderings of the integers with a certain
	invariance property. We describe all such orders in a simple way.
	We define and represent random shuffles of a countable set of labels
	and then give an interpretation of these orders in terms of a class
	of generalized riffle shuffles.},
	author = {Saul Jacka and Jon Warren},
	comments = {12 pages. Cited in math.CO/0508131},
	eprint = {math/0508369},
	oai2identifier = {math/0508369},
	owner = {leo},
	timestamp = {2009.03.12},
	title = {Random orderings of the integers and card shuffling},
	url = {http://arxiv.org/pdf/math.PR/0508369},
	year = {2005},
	bdsk-url-1 = {http://arxiv.org/pdf/math.PR/0508369}}

@article{Jacobi1841,
	author = {Jacobi, C. G. J.},
	date-added = {2013-10-12 16:09:09 +0000},
	date-modified = {2013-10-12 16:10:28 +0000},
	journal = {Crelle's Journal},
	note = {Reprinted in Gesammelte Werke 3, 439--452, Chelsea, New York, 1969.},
	pages = {360-371},
	title = {{De functionibus alternantibus earumque divisione per productum e differentiis elementorum conflatum}},
	volume = {22},
	year = {1841}}

@book{James1978,
	author = {G.D. James},
	owner = {leo},
	publisher = {Lecture Notes in Mathematics 682, Springer-Verlag},
	timestamp = {2009.04.28},
	title = {The {R}epresentation {T}heory of the {S}ymmetric {G}roups},
	year = {1978}}

@article{Jelinek1992,
	author = {Jelinek, F. and Lafferty, J.D. and Mercer, R.L.},
	journal = {Speech Recognition and Understanding: Recent Advances, Trends, and Applications},
	title = {{Basic methods of probabilistic context free grammars}},
	volume = {75},
	year = {1992}}

@inproceedings{Jirina1964,
	author = {Jirina, M.},
	booktitle = {Trans. Third Prague Conf. on Inf. Th.},
	date-added = {2011-11-05 14:18:53 +0000},
	date-modified = {2011-11-05 14:19:49 +0000},
	pages = {333-357},
	title = {Branching processes with measure-valued states},
	year = {1964}}

@article{Johansson2000,
	address = {Basel},
	author = {Johansson, Kurt},
	journal = {European Congress of Mathematics, Vol. I (Barcelona, 2000)},
	owner = {leo},
	pages = {445--456},
	publisher = {Birkh\"auser},
	series = {Progr. Math.},
	timestamp = {2009.10.13},
	title = {Random Growth and Random Matrices},
	volume = {201},
	year = {2000}}

@article{Johansson2005lectures,
	author = {Johansson, K.},
	date-added = {2013-04-09 02:21:33 +0000},
	date-modified = {2013-04-09 02:21:55 +0000},
	note = {arXiv:math-ph/0510038},
	title = {Random matrices and determinantal processes},
	year = {2005}}

@article{johansson2005non,
	author = {Johansson, K.},
	date-modified = {2012-02-03 01:25:35 +0000},
	journal = {Annales de l'Institut Fourier (Grenoble)},
	note = {arXiv:math/0409013 [math.PR]},
	number = {6},
	pages = {2129--2145},
	title = {{Non-intersecting, simple, symmetric random walks and the extended Hahn kernel}},
	volume = {55},
	year = {2005}}

@article{johansson2003discrete,
	author = {Johansson, K.},
	date-modified = {2018-03-12 18:58:09 +0000},
	journal = {Commun. Math. Phys.},
	note = {arXiv:math/0206208 [math.PR]},
	number = {1},
	pages = {277-329},
	title = {{Discrete polynuclear growth and determinantal processes}},
	volume = {242},
	year = {2003}}

@article{johansson2002non,
	author = {Johansson, K.},
	date-modified = {2018-02-28 19:39:25 +0000},
	journal = {Probab. Theory Relat. Fields},
	note = {arXiv:math/0011250 [math.PR]},
	number = {2},
	pages = {225--280},
	publisher = {Springer},
	title = {{Non-intersecting paths, random tilings and random matrices}},
	volume = {123},
	year = {2002}}

@article{Johansso1999Plancherel,
	author = {Johansson, K.},
	date-added = {2011-04-22 10:09:49 +0400},
	date-modified = {2016-05-04 16:39:25 +0000},
	journal = {Ann. Math.},
	number = {1},
	pages = {259-296},
	title = {{Discrete orthogonal polynomial ensembles and the Plancherel measure}},
	volume = {153},
	year = {2001}}

@article{Johansson1999,
	author = {Johansson, K.},
	date-modified = {2016-05-04 16:39:33 +0000},
	journal = {Ann. Math.},
	note = {arXiv:math/9906120 [math.CO]},
	number = {1},
	owner = {leo},
	pages = {259-296},
	timestamp = {2009.12.11},
	title = {{Discrete orthogonal polynomial ensembles and the Plancherel measure}},
	volume = {153},
	year = {2001}}

@article{johansson2000shape,
	author = {Johansson, K.},
	date-modified = {2016-08-08 00:46:49 +0000},
	journal = {Commun. Math. Phys.},
	note = {arXiv:math/9903134 [math.CO]},
	number = {2},
	pages = {437--476},
	publisher = {Springer},
	title = {{Shape fluctuations and random matrices}},
	volume = {209},
	year = {2000}}

@article{johansson2006eigenvalues,
	author = {Johansson, K. and Nordenstam, E.},
	date-modified = {2018-02-28 19:50:15 +0000},
	journal = {Electron. J. Probab.},
	note = {arXiv:math/0606760 [math.PR]},
	number = {50},
	pages = {1342--1371},
	title = {{Eigenvalues of GUE minors}},
	volume = {11},
	year = {2006}}

@article{johansson2006eigenvaluesErratum,
	author = {Johansson, K. and Nordenstam, E.},
	date-modified = {2018-02-28 19:50:15 +0000},
	journal = {Electron. J. Probab.},
	number = {37},
	pages = {1048--1051},
	title = {Erratum to Eigenvalues of GUE Minors},
	volume = {12},
	year = {2007}}

@phdthesis{Nordenstam2009Thesis,
	author = {Nordenstam, E.},
	school = {KTH},
	title = {Interlaced particles in tilings and random matrices},
	year = {2009}}

@article{novak2015lozenge,
	author = {Novak, J.},
	date-modified = {2018-02-28 19:41:34 +0000},
	journal = {J. Stat. Phys},
	note = {arXiv:1407.7578 [math-ph]},
	number = {2},
	pages = {509--517},
	title = {Lozenge tilings and Hurwitz numbers},
	volume = {161},
	year = {2015}}

@article{Panova2014Free,
	author = {Panova, G.},
	journal = {Letters in Mathematical Physics},
	note = {arXiv:1407.7578 [math-ph]},
	number = {11},
	pages = {1551-1586},
	title = {Lozenge Tilings with Free Boundaries},
	volume = {105},
	year = {2015}}

@article{Mkrtchyan2014Periodic,
	author = {Mkrtchyan, S.},
	journal = {Letters in Mathematical Physics},
	note = {arXiv:1309.4825 [math.PR]},
	number = {9},
	pages = {1053-1078},
	title = {Plane partitions with 2-periodic weights},
	volume = {104},
	year = {2014}}

@article{JohanssonNord2006GUEM,
	author = {Johansson, K. and Nordenstam, E.},
	date-added = {2012-10-17 16:33:56 +0000},
	date-modified = {2018-02-28 19:49:30 +0000},
	doi = {10.1214/EJP.v11-370},
	fjournal = {Electron. J. Probab.},
	issn = {1083-6489},
	journal = {Electron. J. Probab.},
	mrclass = {60G55 (15A52 52C20 82B44)},
	mrnumber = {2268547 (2008d:60066a)},
	mrreviewer = {Paulo E. Oliveira},
	pages = {no. 50, 1342--1371},
	title = {Eigenvalues of {GUE} minors},
	url = {http://dx.doi.org/10.1214/EJP.v11-370},
	volume = {11},
	year = {2006},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=2268547},
	bdsk-url-2 = {http://dx.doi.org/10.1214/EJP.v11-370}}

@article{Johnson2007,
	author = {Johnson, M. and Griffiths, T.L. and Goldwater, S.},
	journal = {Advances in neural information processing systems},
	pages = {641},
	publisher = {Citeseer},
	title = {{Adaptor grammars: A framework for specifying compositional nonparametric Bayesian models}},
	volume = {19},
	year = {2007}}

@book{Kac1990InfiniteDim,
	address = {Cambridge},
	author = {Kac, Victor G.},
	date-added = {2011-11-07 17:23:15 +0000},
	date-modified = {2011-11-07 17:23:27 +0000},
	doi = {10.1017/CBO9780511626234},
	edition = {Third edition},
	isbn = {0-521-37215-1; 0-521-46693-8},
	mrclass = {17B65 (17B67 17B68 58F07)},
	mrnumber = {1104219 (92k:17038)},
	pages = {xxii+400},
	publisher = {Cambridge University Press},
	title = {Infinite-dimensional {L}ie algebras},
	url = {http://dx.doi.org/10.1017/CBO9780511626234},
	year = {1990},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=1104219},
	bdsk-url-2 = {http://dx.doi.org/10.1017/CBO9780511626234}}

@article{Kardar1987,
	author = {Kardar, M.},
	date-added = {2013-09-08 13:07:18 +0000},
	date-modified = {2013-09-08 13:07:50 +0000},
	journal = {Nuclear Physics B},
	pages = {582-602},
	title = {{Replica Bethe ansatz studies of two-dimensional interfaces with quenched random impurities}},
	volume = {290},
	year = {1987}}

@book{Karlin1968,
	author = {Karlin, S.},
	date-added = {2012-11-02 14:39:41 +0000},
	date-modified = {2012-11-02 14:40:13 +0000},
	publisher = {Stanford},
	title = {{Total positivity, Vol.1}},
	year = {1968}}

@article{Karlin1967number,
	author = {Karlin, S. and McGregor, J.},
	booktitle = {Proceedings of the Fifth Berkeley Symposium on mathematics, Statistics and probability},
	pages = {415--438},
	title = {{The number of mutant forms maintained in a population}},
	volume = {4},
	year = {1967}}

@article{KMG59-Coincidence,
	author = {Karlin, S. and McGregor, J.},
	journal = {Pacific J. Math.},
	owner = {leo},
	pages = {1141-1164},
	timestamp = {2010.08.14},
	title = {Coincidence probabilities},
	volume = {9},
	year = {1959}}

@article{KMG58Linear,
	author = {S. Karlin and J. McGregor},
	journal = {J. Math. Mech.},
	owner = {leo},
	pages = {643-662},
	timestamp = {2010.08.12},
	title = {Linear growth, birth and death processes},
	volume = {7},
	year = {1958}}

@article{KMG57BDClassif,
	author = {S. Karlin and J. McGregor},
	date-modified = {2018-02-28 19:44:38 +0000},
	journal = {Trans. AMS},
	owner = {leo},
	pages = {366-400},
	timestamp = {2010.08.12},
	title = {The classification of birth and death processes},
	volume = {86},
	year = {1957}}

@book{karlin1981second,
	author = {Karlin, S. and Taylor, H.M.},
	publisher = {Academic press},
	title = {{A second course in stochastic processes}},
	year = {1999}}

@incollection{Kasteleyn1967,
	address = {London},
	author = {Kasteleyn, P.},
	booktitle = {{Graph Theory and Theoretical Physics}},
	date-added = {2012-02-03 19:21:21 +0000},
	date-modified = {2012-02-03 19:22:41 +0000},
	pages = {43-110},
	publisher = {Academic Press},
	title = {Graph theory and crystal physics},
	year = {1967}}

@book{Kato1980,
	address = {New York},
	author = {Kato, T.},
	date-added = {2013-01-21 02:43:25 +0000},
	date-modified = {2013-01-21 02:44:13 +0000},
	edition = {2nd},
	publisher = {Springer-Verlag},
	title = {Perturbation theory of linear operators},
	year = {1980}}

@article{Katori2005PfDyn,
	author = {Katori, M.},
	journal = {RIMS Kokyuroku},
	note = {arXiv:math/0506186 [math.PR]},
	owner = {leo},
	pages = {12-25},
	timestamp = {2010.11.14},
	title = {{Non-colliding system of Brownian particles as Pfaffian process}},
	volume = {1422},
	year = {2005}}

@incollection{NagaoKatoriTanemura2004PfDyn,
	author = {Katori, M. and Nagao, T. and Tanemura, H.},
	booktitle = {{Adv. Stud. in Pure Math. 39 ``Stochastic Analysis on Large Scale Interacting Systems''}},
	journal = {Adv. Stud. in Pure Math.},
	owner = {leo},
	pages = {283-306, arXiv:math.PR/0301143},
	publisher = {Mathematical Society of Japan},
	timestamp = {2010.11.14},
	title = {{Infinite systems of non-colliding Brownian particles}},
	year = {2004}}

@article{Katori2010,
	abstract = {A noncolliding diffusion process is a conditional process of $N$ independent
	one-dimensional diffusion processes such that the particles never
	collide with each other. This process realizes an interacting particle
	system with long-ranged strong repulsive forces acting between any
	pair of particles. When the individual diffusion process is a one-dimensional
	Brownian motion, the noncolliding process is equivalent in distribution
	with the eigenvalue process of an $N \times N$ Hermitian-matrix-valued
	process, which we call Dyson's model. For any deterministic initial
	configuration of $N$ particles, distribution of particle positions
	of the noncolliding Brownian motion on the real line at any fixed
	time $t >0$ is a determinantal point process. We can prove that the
	process is determinantal in the sense that the multi-time correlation
	function for any chosen series of times, which determines joint distributions
	at these times, is also represented by a determinant. We study the
	asymptotic behavior of the system, when the number of Brownian motions
	$N$ in the system tends to infinity. This problem is concerned with
	the random matrix theory on the asymptotics of eigenvalue distributions,
	when the matrix size becomes infinity. In the present paper, we introduce
	a variety of noncolliding diffusion processes by generalizing the
	noncolliding Brownian motion, some of which are temporally inhomogeneous.
	We report the results of our research project to construct and study
	finite and infinite particle systems with long-ranged strong interactions
	realized by noncolliding processes.},
	author = {Makoto Katori and Hideki Tanemura},
	comments = {AMS-LaTeX, 32 pages, 3 figures, 3 tables, to be published in Sugaku Expositions (AMS)},
	eprint = {1005.0533},
	oai2identifier = {1005.0533},
	owner = {leo},
	timestamp = {2010.05.17},
	title = {Noncolliding processes, matrix-valued processes and determinantal processes},
	year = {2010}}

@article{Kenyon2007Lecture,
author = {Kenyon, R.},
journal = {arXiv preprint},
note = {arXiv:0910.3129 [math.PR]},
title = {{Lectures on dimers}},
year = {2009}
}


@article{Kenyon2004Height,
	author = {Kenyon, R.},
	date-added = {2012-02-02 21:19:47 +0000},
	date-modified = {2016-08-02 03:00:33 +0000},
	journal = {Commun. Math. Phys.},
	note = {arXiv:math-ph/0405052},
	number = {3},
	pages = {675--709},
	title = {Height fluctuations in the honeycomb dimer model},
	volume = {281},
	year = {2008}}

@article{Kenyon2001GFF,
	author = {Kenyon, R.},
	date-added = {2012-02-03 02:49:54 +0000},
	date-modified = {2018-02-28 19:46:40 +0000},
	journal = {Ann. Probab.},
	note = {arXiv:math-ph/0002027},
	number = {3},
	pages = {1128--1137},
	title = {{Dominos and the Gaussian Free Field}},
	volume = {29},
	year = {2001}}

@article{Kenyon2000Conformal,
	author = {Kenyon, R.},
	date-added = {2012-03-06 01:31:04 +0000},
	date-modified = {2016-05-04 16:39:43 +0000},
	journal = {{Ann. Probab.}},
	note = {arXiv:math-ph/9910002},
	number = {2},
	pages = {759--795},
	title = {Conformal invariance of domino tiling},
	volume = {28},
	year = {2000}}

@article{Kenyon1997LocalStat,
	author = {Kenyon, R.},
	date-added = {2012-02-03 00:32:30 +0000},
	date-modified = {2012-02-03 00:33:17 +0000},
	journal = {Annales de Inst. H. Poincar\'e, Probabilit\'es et Statistiques},
	note = {arXiv:math/0105054 [math.CO]},
	pages = {591--618},
	title = {Local statistics of lattice dimers},
	volume = {33},
	year = {1997}}

@article{OkounkovKenyon2007Limit,
	author = {Kenyon, R. and Okounkov, A.},
	date-added = {2012-01-12 21:58:35 +0000},
	date-modified = {2012-02-02 20:53:54 +0000},
	journal = {Acta Math.},
	note = {arXiv:math-ph/0507007},
	number = {2},
	pages = {263--302},
	title = {Limit shapes and the complex {B}urgers equation},
	volume = {199},
	year = {2007},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=2358053}}

@article{KOS2006,
	author = {Kenyon, R. and Okounkov, A. and Sheffield, S.},
	date-added = {2012-02-03 00:30:59 +0000},
	date-modified = {2012-02-03 00:31:37 +0000},
	journal = {Ann. Math.},
	note = {arXiv:math-ph/0311005},
	pages = {1019--1056},
	title = {Dimers and amoebae},
	volume = {163},
	year = {2006}}

@book{Kerov-book,
	author = {S. Kerov},
	owner = {leo},
	publisher = {AMS, Translations of Mathematical Monographs},
	timestamp = {2009.04.15},
	title = {Asymptotic Representation Theory of the Symmetric Group and its Applications in Analysis},
	volume = {219},
	year = {2003}}

@article{Kerov2000,
	abstract = {We study the Young graph with edge multiplicities arising in a Pieri-type
	formula for Jack symmetric polynomials $P_\mu(x;a)$ with a parameter
	$a$. Starting with the empty diagram, we define recurrently the `dimensions'
	$\dim_a$ in the same way as for the Young lattice or Pascal triangle.
	New proofs are given for two known results. The first is the $a$-hook
	formula for $\dim_a$, first found by R.Stanley. Secondly, we prove
	(for all complex $u$ and $v$) a generalization of the identity $\sum\nu(c(b)+u)(c(b)+v)\dim\nu/\dim\mu=(n+1)(n+uv)$,
	where $\nu$ runs over immediate successors of a Young diagram $\mu$
	with $n$ boxes. Here $c(b)$ is the content of a new box $b$. The
	identity is known to imply the existence of an interesting family
	of positive definite central functions on the infinite symmetric
	group. The approach is based on the interpretation of a Young diagram
	as a pair of interlacing sequences, so that analytic techniques may
	be used to solve combinatorial problems. We show that when dealing
	with Jack polynomials $P_\mu(x;a)$, it makes sense to consider `anisotropic'
	Young diagrams made of rectangular boxes of size $1\times a$.},
	author = {Kerov, S.},
	comments = {16 pages, AmSTeX, uses EPSF, three EPS figures},
	date-modified = {2011-11-14 16:55:11 +0000},
	eprint = {math/9712267},
	journal = {Functional Analysis and Its Applications},
	note = {arXiv:math/9712267 [math.CO]},
	number = {1},
	oai2identifier = {math/9712267},
	owner = {leo},
	pages = {41-51},
	reportno = {PDMI 24/1997},
	timestamp = {2009.03.26},
	title = {Anisotropic {Y}oung diagrams and {J}ack symmetric functions},
	url = {http://arxiv.org/abs/math/9712267},
	volume = {34},
	year = {2000},
	bdsk-url-1 = {http://arxiv.org/abs/math/9712267}}

@article{Kerov1996YoungBoundary,
	author = {Kerov, S.},
	date-added = {2011-08-03 07:13:10 +0000},
	date-modified = {2011-08-03 07:13:49 +0000},
	journal = {S{\'e}ries formelles et combinatoire alg{\'e}brique},
	title = {The boundary of Young lattice and random Young tableaux},
	volume = {24},
	year = {1994}}

@article{kerov1993gaussian,
	author = {Kerov, S.},
	issn = {0764-4442},
	journal = {Comptes rendus de l'Acad{\'e}mie des sciences. S{\'e}rie 1, Math{\'e}matique},
	number = {4},
	pages = {303--308},
	publisher = {Elsevier},
	title = {{Gaussian limit for the Plancherel measure of the symmetric group}},
	volume = {316},
	year = {1993}}

@article{Kerov1992,
	author = {S. Kerov},
	journal = {Funkts. Anal. Prilozh.},
	number = {3},
	owner = {leo},
	pages = {35-45},
	timestamp = {2009.05.06},
	title = {A $q$-analog of the hook walk algorithm and random {Y}oung tableaux},
	volume = {26},
	year = {1992}}

@article{Kerov1992HL,
	author = {Kerov, S.},
	date-added = {2014-01-19 18:30:49 +0000},
	date-modified = {2014-01-19 18:31:35 +0000},
	journal = {Adv. Sov. Math.},
	pages = {67-94},
	title = {{Generalized Hall-Littlewood symmetric functions and orthogonal polynomials}},
	volume = {9},
	year = {1992}}

@article{Kerov1987,
	author = {Kerov, S.V.},
	date-added = {2011-06-15 12:38:03 +0400},
	date-modified = {2011-06-15 12:39:34 +0400},
	journal = {Journal of Mathematical Sciences},
	number = {2},
	pages = {2503-2507},
	title = {{Realizations of representations of a Brauer semigroup}},
	volume = {47},
	year = {1989}}

@article{Kerov1989,
	author = {Kerov, S.},
	date-modified = {2011-09-18 22:21:34 +0000},
	journal = {Zapiski Nauchn. Semin. LOMI},
	note = {English translation: J. Soviet Math., {\bf{}59\/} (1992), 1063-1071.},
	owner = {leo},
	pages = {55-67},
	timestamp = {2009.04.27},
	title = {{Combinatorial examples in the theory of AF-algebras}},
	volume = {172},
	year = {1989}}

@article{kerov1986distribution,
	author = {Kerov, S.},
	date-added = {2011-09-18 06:24:24 +0000},
	date-modified = {2011-09-18 06:25:17 +0000},
	journal = {Zapiski Nauchnyh Seminarov LOMI},
	note = {English translation in J. Soviet Math. (New York) {\bf{}41\/} (1988), no. 2, 995--999.},
	pages = {181--186},
	title = {Distribution of symmetry types of high rank tensors},
	volume = {155},
	year = {1986}}

@article{Kerov1998,
	author = {Kerov, S. and Okounkov, A. and Olshanski, G.},
	date-modified = {2018-02-28 19:47:33 +0000},
	journal = {Int. Math. Res. Notices},
	note = {arXiv:q-alg/9703037},
	pages = {173-199},
	title = {{The boundary of Young graph with Jack edge multiplicities}},
	volume = {4},
	year = {1998},
	bdsk-url-1 = {http://arxiv.org/abs/q-alg/9703037}}

@article{Kerov2004,
	abstract = {Let S be the group of finite permutations of the naturals 1,2,...
	The subject of the paper is harmonic analysis for the Gelfand pair
	(G,K), where G stands for the product of two copies of S while K
	is the diagonal subgroup in G. The spherical dual to (G,K) (that
	is, the set of irreducible spherical unitary representations) is
	an infinite-dimensional space. For such Gelfand pairs, the conventional
	scheme of harmonic analysis is not applicable and it has to be suitably
	modified. We construct a compactification of S called the space of
	virtual permutations. It is no longer a group but it is still a G-space.
	On this space, there exists a unique G-invariant probability measure
	which should be viewed as a true substitute of Haar measure. More
	generally, we define a 1-parameter family of probability measures
	on virtual permutations, which are quasi-invariant under the action
	of G. Using these measures we construct a family {T_z} of unitary
	representations of G depending on a complex parameter z. We prove
	that any T_z admits a unique decomposition into a multiplicity free
	integral of irreducible spherical representations of (G,K). Moreover,
	the spectral types of different representations (which are defined
	by measures on the spherical dual) are pairwise disjoint. Our main
	result concerns the case of integral values of parameter z: then
	we obtain an explicit decomposition of T_z into irreducibles. The
	case of nonintegral z is quite different. It was studied by Borodin
	and Olshanski, see e.g. the survey math.RT/0311369.},
	author = {Kerov, S. and Olshanski, G. and Vershik, A.},
	comments = {AMS Tex, 80 pages, no figures},
	eprint = {math/0312270},
	journal = {Invent. Math.},
	note = {arXiv:math/0312270 [math.RT]},
	number = {3},
	oai2identifier = {math/0312270},
	owner = {leo},
	pages = {551-642},
	timestamp = {2009.03.27},
	title = {Harmonic analysis on the infinite symmetric group},
	url = {http://arxiv.org/abs/math/0312270},
	volume = {158},
	year = {2004},
	bdsk-url-1 = {http://arxiv.org/abs/math/0312270}}

@article{KOV2004,
	author = {Kerov, S. and Olshanski, G. and Vershik, A.},
	journal = {Inventiones mathematicae},
	number = {3},
	pages = {551--642},
	publisher = {Springer},
	title = {{Harmonic analysis on the infinite symmetric group}},
	volume = {158},
	year = {2004}}

@article{Kerov1993,
	author = {Kerov, S. and Olshanski, G. and Vershik, A.},
	journal = {Comptes Rendus Acad. Sci. Paris Ser. I},
	owner = {leo},
	pages = {773-778},
	timestamp = {2009.03.27},
	title = {Harmonic analysis on the infinite symmetric group. {A} deformation of the regular representation},
	volume = {316},
	year = {1993}}

@article{Khesin2012Pentagram,
	author = {Khesin, B. and Soloviev, F.},
	date-added = {2012-09-23 12:29:29 +0000},
	date-modified = {2012-09-23 12:29:59 +0000},
	title = {{The Pentagram map in higher dimensions and KdV flows}},
	year = {2012}}

@article{Khesin2012Pentagram2,
	author = {Khesin, B. and Soloviev, F.},
	date-added = {2012-09-23 12:29:29 +0000},
	date-modified = {2012-09-23 12:30:21 +0000},
	title = {{Integrability of higher pentagram maps}},
	year = {2012},
	bdsk-url-1 = {http://arxiv.org/abs/1204.0756}}

@article{Khorunzhy2001,
	abstract = {We describe one interpretation of the q-Catalan numbers in frameworks
	of random matrix theory and weighted partitions of the set of integers.},
	author = {A. Khorunzhy},
	comments = {7 pages, LaTeX},
	eprint = {math/0104074},
	oai2identifier = {math/0104074},
	owner = {leo},
	timestamp = {2009.05.11},
	title = {Products of random matrices and q-Catalan numbers},
	year = {2001}}

@article{Khoruzhenko2009,
	abstract = {This is a concise review of the complex, real and quaternion real
	Ginibre random matrix ensembles and their elliptic deformations.
	Eigenvalue correlations are exactly reduced to two-point kernels
	and discussed in the strongly and weakly non-Hermitian limits of
	large matrix size.},
	author = {B. A. Khoruzhenko and H. -J. Sommers},
	comments = {23 pages, invited article for the Oxford Handbook of Random Matrix Theory},
	eprint = {0911.5645},
	oai2identifier = {0911.5645},
	owner = {leo},
	timestamp = {2010.11.01},
	title = {Non-Hermitian Random Matrix Ensembles},
	year = {2009}}

@article{Khovanova2008,
	abstract = {I show how to associate a Clifford algebra to a graph. I describe
	the structure of these Clifford graph algebras and provide many examples
	and pictures. I describe which graphs correspond to isomorphic Clifford
	algebras and also discuss other related sets of graphs. This construction
	can be used to build models of representations of simply-laced compact
	Lie groups.},
	author = {Tanya Khovanova},
	comments = {19 pages, 12 figures},
	eprint = {0810.3322},
	oai2identifier = {0810.3322},
	owner = {leo},
	timestamp = {2010.05.30},
	title = {Clifford Algebras and Graphs},
	year = {2008}}

@article{Kim1999,
	author = {Jeong Han Kim and Boris Pittel},
	owner = {leo},
	timestamp = {2009.05.11},
	title = {Confirming {K}leitman--{W}inston conjecture on the largest coefficient in a q-{C}atalan number},
	year = {1999}}

@book{Kingman1993,
	author = {J. F. C. Kingman},
	owner = {leo},
	publisher = {Clarendon Press},
	timestamp = {2009.08.13},
	title = {Poisson {P}rocesses},
	year = {1993}}

@article{Kingman1978,
	author = {J. F. C. Kingman},
	journal = {Proc. R. Soc. London, A},
	owner = {leo},
	pages = {1-20},
	timestamp = {2009.03.27},
	title = {Random partitions in population genetics},
	volume = {361},
	year = {1978}}

@article{Kingman1975,
	author = {J. F. C. Kingman},
	journal = {J. Roy. Statist. Soc. B},
	owner = {leo},
	pages = {1-22},
	timestamp = {2010.01.12},
	title = {Random discrete distributions},
	volume = {37},
	year = {1975}}

@inproceedings{Kirillov2000_Tropical,
	address = {Singapore},
	author = {Kirillov, A.N.},
	booktitle = {Physics and Combinatorics, Proceedings of the Nagoya 2000 International Workshop},
	date-added = {2013-05-03 03:19:34 +0000},
	date-modified = {2013-05-03 03:21:21 +0000},
	editor = {Kirillov, A.N. and Liskova, N.},
	pages = {82-150},
	publisher = {World Scientific},
	title = {{Introduction to tropical combinatorics}},
	year = {2001}}

@book{Kirillov_orbit,
	author = {Kirillov, A.A.},
	date-added = {2013-10-14 18:17:38 +0000},
	date-modified = {2013-10-14 18:18:53 +0000},
	publisher = {Amer. Math. Soc.},
	title = {{Lectures on the orbit method}},
	volume = {64},
	year = {2004}}

@article{Kirillov1989identities,
	author = {Kirillov, A.N.},
	date-added = {2012-09-23 12:17:13 +0000},
	date-modified = {2012-09-23 12:17:32 +0000},
	journal = {Journal of Mathematical Sciences},
	number = {2},
	pages = {2450--2459},
	publisher = {Springer},
	title = {{Identities for the Rogers dilogarithm function connected with simple Lie algebras}},
	volume = {47},
	year = {1989}}

@article{KirillovReshetikhin1987QSystems,
	author = {Kirillov, A.N. and Reshetikhin, N.Y.},
	date-added = {2012-09-23 00:43:33 +0000},
	date-modified = {2012-09-23 12:16:00 +0000},
	journal = {Journal of mathematical sciences},
	note = {Translated from Zap. Nauch. Sem. LOMI, 160 (1987), 211-221},
	number = {3},
	pages = {3156--3164},
	publisher = {Springer},
	title = {{Representations of Yangians and multiplicities of occurrence of the irreducible components of the tensor product of representations of simple Lie algebras}},
	volume = {52},
	year = {1990}}

@article{SmirnovSchubert2012,
	author = {Kiritchenko, V. and Smirnov, E. and Timorin, V.},
	date-added = {2013-05-03 19:38:36 +0000},
	date-modified = {2013-05-03 19:40:12 +0000},
	journal = {Russian Mathematical Surveys},
	note = {arXiv:1101.0278 [math.AG]},
	number = {4},
	pages = {685-719},
	title = {{Schubert calculus and Gelfand-Zetlin polytopes}},
	volume = {67},
	year = {2012}}

@article{Klarner1970,
	author = {Klarner, David A},
	journal = {J. Combinatorial Theory},
	owner = {leo},
	pages = {401-411},
	timestamp = {2009.06.12},
	title = {Correspondences between plane trees and binary sequences},
	volume = {9},
	year = {1970}}

@book{kleshchev2005linear,
	author = {Kleshch{\\"e}v, A.S.},
	publisher = {Cambridge Univ Pr},
	title = {{Linear and projective representations of symmetric groups}},
	year = {2005}}

@book{Knuth1973art3,
	address = {London},
	author = {Knuth, D.E.},
	date-added = {2013-04-06 22:12:20 +0000},
	date-modified = {2013-04-06 22:13:17 +0000},
	publisher = {Addison--Wesley},
	title = {{The Art of Computer Programming, Vol. 3: Sorting and Searching}},
	year = {1973}}

@article{Knuth1970,
	author = {Donald Knuth},
	date-modified = {2020-04-19 13:23:36 -0400},
	journal = {Pacific J. Math.},
	number = {3},
	owner = {leo},
	pages = {709-727},
	timestamp = {2009.05.12},
	title = {{Permutations, matrices, and generalized Young tableaux}},
	volume = {34},
	year = {1970}}

@article{Knuth1992,
	abstract = {The author advocates two specific mathematical notations from his
	popular course and joint textbook, "Concrete Mathematics". The first
	of these, extending an idea of Iverson, is the notation "[P]" for
	the function which is 1 when the Boolean condition P is true and
	0 otherwise. This notation can encourage and clarify the use of characteristic
	functions and Kronecker deltas in sums and integrals. The second
	notation puts Stirling numbers on the same footing as binomial coefficients.
	Since binomial coefficients are written on two lines in parentheses
	and read "n choose k", Stirling numbers of the first kind should
	be written on two lines in brackets and read "n cycle k", while Stirling
	numbers of the second kind should be written in braces and read "n
	subset k". (I might say "n partition k".) The written form was first
	suggested by Imanuel Marx. The virtues of this notation are that
	Stirling partition numbers frequently appear in combinatorics, and
	that it more clearly presents functional relations similar to those
	satisfied by binomial coefficients.},
	author = {Donald E. Knuth},
	comments = {Abstract added by Greg Kuperberg},
	eprint = {math/9205211},
	journal = {Amer. Math. Monthly},
	number = {5},
	oai2identifier = {math/9205211},
	owner = {leo},
	pages = {403--422},
	reportno = {Knuth migration 11/2004},
	timestamp = {2009.09.03},
	title = {Two notes on notation},
	volume = {99},
	year = {1992}}

@book{Koekoek_book,
	author = {Koekoek, R. and Lesky, P. and Swarttouw, R.},
	publisher = {Springer},
	title = {Hypergeometric orthogonal polynomials and their q-analogues},
	year = {2010}}

@article{Koekoek1996,
	author = {Koekoek, R. and Swarttouw, R.F.},
	note = {arXiv:math/9602214 [math.CA], report no. OP-SF 20 Feb 1996. Updated version available at \url{https://fa.ewi.tudelft.nl/~koekoek/documents/as98.pdf}},
	journal = {Technical report, Delft University of Technology and Free University of Amsterdam},
	title = {{The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue}},
	year = {1996}}

@article{Kogan2002RSK,
	author = {M. Kogan and A. Kumar},
	journal = {Proc. AMS},
	number = {9},
	owner = {leo},
	pages = {2525-2534},
	timestamp = {2010.04.15},
	title = {{A proof of Pieri's formula using the generalized Schensted insertion algorithm for RC-graphs}},
	volume = {130},
	year = {2002}}

@article{kondratiev2002heat,
	abstract = {In this paper, we study properties of the heat semigroup of configuration
	space analysis. Using a natural ``Riemannian-like'' structure of
	the configuration space $\Gamma_X$ over a complete, connected, oriented,
	and stochastically complete Riemannian manifold $X$ of infinite volume,
	the heat semigroup $(e^{-tH^\Gamma})_{t\in\R_+}$ was introduced and
	studied in [{\it J. Func. Anal.} {\bf 154} (1998), 444--500]. Here,
	$H^\Gamma$ is the Dirichlet operator of the Dirichlet form ${\cal
	E}^\Gamma$ over the space $L^2(\Gamma_X,\pi_m)$, where $\pi_m$ is
	the Poisson measure on $\Gamma_X$ with intensity $m$--the volume
	measure on $X$. We construct a metric space $\Gamma_\infty$ that
	is continuously embedded into $\Gamma_X$. Under some conditions on
	the manifold $X$ and we prove that $\Gamma_\infty$ is a set of full
	$\pi_m$ measure. The central results of the paper are two types of
	Feller properties for the heat semigroup. Next, we give a direct
	construction of the independent infinite particle process on the
	manifold $X$, which is a realization of the Brownian motion on the
	configuration space. The main point here is that we prove that this
	process can start in every $\gamma\in\Gamma_\infty$, will never leave
	$\Gamma_\infty$, and has continuous sample path in $\Gamma_\infty$,
	provided $\operatorname{dim}X\ge2$. In this case, we also prove that
	this process is a strong Markov process whose transition probabilities
	are given by the $\P_{t,\gamma}(\cdot)$ above. Furthermore, we discuss
	the necessary changes to be done for constructing the process in
	the case $\operatorname{dim}X=1$. Finally, as an easy consequence
	we get a ``path-wise'' construction of the independent particle process
	on $\Gamma_\infty$ from the underlying Brownian motion.},
	author = {Kondratiev, Y. and Lytvynov, E. and {R\"ockner}, M.},
	eprint = {math/0211325},
	journal = {Publications of the Research Institute for Mathematical Sciences},
	oai2identifier = {math/0211325},
	owner = {leo},
	pages = {1--48},
	timestamp = {2010.04.29},
	title = {The heat semigroup on configuration spaces},
	volume = {39},
	year = {2003}}

@article{Koornwinder1982Krawtchouk,
	author = {Koornwinder, T.H.},
	coden = {SJMAAH},
	date-added = {2011-11-13 01:04:38 +0000},
	date-modified = {2011-11-14 16:56:04 +0000},
	doi = {10.1137/0513072},
	fjournal = {SIAM Journal on Mathematical Analysis},
	issn = {0036-1410},
	journal = {SIAM J. Math. Anal.},
	number = {6},
	pages = {1011--1023},
	title = {Krawtchouk polynomials, a unification of two different group theoretic interpretations},
	url = {http://dx.doi.org/10.1137/0513072},
	volume = {13},
	year = {1982},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=674770},
	bdsk-url-2 = {http://dx.doi.org/10.1137/0513072}}

@article{Kovchegov2008,
	abstract = {In this article, we will explore why Karlin-McGregor method of using
	orthogonal polynomials in the study of Markov processes was so successful
	for one dimensional nearest neighbor processes, but failed beyond
	nearest neighbor transitions. We will proceed by suggesting and testing
	possible fixtures.},
	author = {Yevgeniy Kovchegov},
	comments = {12 pages},
	eprint = {0812.1779},
	oai2identifier = {0812.1779},
	owner = {leo},
	timestamp = {2009.04.03},
	title = {Orthogonality and probability: beyond nearest neighbor transitions},
	url = {http://arxiv.org/abs/0812.1779},
	year = {2008},
	bdsk-url-1 = {http://arxiv.org/abs/0812.1779}}

@article{Krasovsky1998qHahn,
	author = {Krasovsky, I.V.},
	date-added = {2011-08-03 08:11:43 +0000},
	date-modified = {2011-08-03 08:12:19 +0000},
	note = {arXiv:physics/9802045 [math-ph]},
	title = {Quasi-exactly solvable problems and the dual (q-)Hahn polynomials},
	year = {1998}}

@article{krattenthaler1999advanced,
	author = {Krattenthaler, C.},
	date-added = {2012-11-05 14:45:50 +0000},
	date-modified = {2020-06-19 12:04:53 -0400},
	journal = {S{\'e}minaire Lotharingien Combin},
	note = {arXiv:math/9902004 [math.CO]},
	pages = {B42q},
	title = {Advanced determinant calculus},
	volume = {42},
	year = {1999}}

@article{Kreweras1965,
	author = {G. Kreweras},
	journal = {Cahiers du B.U.R.O.},
	owner = {leo},
	timestamp = {2009.05.29},
	title = {Sur une classe de problemes de denombrement lies au treillis des partitions des entiers},
	volume = {6},
	year = {1965}}

@article{Kuan2011GFF,
	author = {Kuan, J.},
	date-added = {2012-04-03 23:31:17 +0000},
	date-modified = {2018-02-28 19:50:15 +0000},
	journal = {Electron. J. Probab.},
	note = {arXiv:1109.4444 [math-ph]},
	number = {72},
	pages = {1-31},
	title = {{The Gaussian free field in interlacing particle systems}},
	volume = {19},
	year = {2014}}

@article{Kuba2009,
	author = {M. Kuba and A. Panholzer and H. Prodinger},
	date-modified = {2018-02-28 19:49:54 +0000},
	journal = {El. Jour. Combin.},
	owner = {leo},
	pages = {\#R67},
	timestamp = {2009.05.30},
	title = {Lattice paths, sampling without replacement, and limiting distributions},
	volume = {16},
	year = {2009}}

@article{kuniba2011TY_Syst,
	author = {Kuniba, A. and Nakanishi, T. and Suzuki, J.},
	date-added = {2012-09-23 12:04:02 +0000},
	date-modified = {2012-09-23 12:15:48 +0000},
	journal = {Journal of Physics A: Mathematical and Theoretical},
	pages = {103001},
	title = {{T-systems and Y-systems in integrable systems}},
	volume = {44},
	year = {2011}}

@article{Kuniba2002canonical,
	author = {Kuniba, A. and Nakanishi, T.. and Tsuboi, Z.},
	date-added = {2012-09-23 12:20:30 +0000},
	date-modified = {2018-02-28 19:49:00 +0000},
	journal = {Comm. Math. Phys},
	pages = {19--31},
	title = {{The canonical solutions of the Q-systems and the Kirillov-Reshetikhin conjecture}},
	volume = {59},
	year = {2002}}

@article{Kuperberg1994SCPP,
	author = {Kuperberg, G.},
	date-added = {2011-11-07 13:49:16 +0000},
	date-modified = {2011-11-14 16:57:31 +0000},
	journal = {European J. Combin.},
	note = {arXiv:math/9411239 [math.CO]},
	number = {6},
	pages = {545-553},
	title = {{Self-complementary plane partitions by Proctor's minuscule method}},
	volume = {15},
	year = {1994}}

@article{Konig2005,
	author = {K{\"o}nig, W.},
	date-modified = {2011-09-18 06:27:53 +0000},
	journal = {Probab. Surv.},
	note = {arXiv:math/0403090 [math.PR]},
	pages = {385--447},
	title = {{Orthogonal polynomial ensembles in probability theory}},
	volume = {2},
	year = {2005}}

@article{konig2002non,
	author = {K{\"o}nig, W. and O'Connell, N. and Roch, S.},
	date-modified = {2018-02-28 19:50:15 +0000},
	journal = {Electron. J. Probab.},
	number = {5},
	pages = {1-24},
	title = {{Non-colliding random walks, tandem queues, and discrete orthogonal polynomial ensembles}},
	volume = {7},
	year = {2002}}

@article{LakshtanovRoschina2010War,
	author = {Lakshtanov, E. and Roschina, V.},
	date-added = {2011-08-03 06:48:54 +0000},
	date-modified = {2011-08-03 06:50:25 +0000},
	note = {arXiv:1007.1371 [math.DS]},
	title = {Finiteness in the Card Game of War},
	year = {2010}}

@article{Lam2006SignedDiffPosets,
	abstract = {We study signed differential posets, a signed version of differential
	posets. These posets satisfy enumerative identities which are signed
	analogues of those satisfied by differential posets. Our main motivations
	are the sign-imbalance identities for partition shapes originally
	conjectured by Stanley, now proven by Lam, Reifergerste and Sjostrand.
	We show that these identities result from a signed differential poset
	structure on Young's lattice, and explain similar identities for
	Fibonacci shapes.},
	author = {Thomas Lam},
	date-added = {2011-08-03 15:07:54 +0000},
	date-modified = {2011-08-03 15:08:23 +0000},
	eprint = {math/0611296v2},
	note = {arXiv:math/0611296 [math.CO]},
	title = {Signed differential posets and sign-imbalance},
	url = {http://arxiv.org/abs/math/0611296v2},
	bdsk-url-1 = {http://arxiv.org/abs/math/0611296v2}}

@article{Lam2008QuantizedDual,
	abstract = {We study quantized dual graded graphs, which are graphs equipped with
	linear operators satisfying the relation DU - qUD = rI. We construct
	examples based upon: the Fibonacci poset, permutations, standard
	Young tableau, and plane binary trees.},
	author = {Thomas Lam},
	date-added = {2011-08-03 14:38:13 +0000},
	date-modified = {2011-08-03 14:40:34 +0000},
	eprint = {0808.0345v1},
	note = {arXiv:0808.0345 [math.CO]},
	title = {Quantized dual graded graphs},
	url = {http://arxiv.org/abs/0808.0345v1},
	year = {2008},
	bdsk-url-1 = {http://arxiv.org/abs/0808.0345v1}}

@article{Lam2005CombBosonFermion,
	author = {Lam, T.},
	date-added = {2011-08-03 14:34:27 +0000},
	date-modified = {2011-08-03 14:35:03 +0000},
	note = {arXiv:math/0507341 [math.CO]},
	title = {A combinatorial generalization of the Boson-Fermion correspondence},
	year = {2005}}

@article{Lam2003Ribbon,
	author = {Lam, T.},
	date-added = {2011-08-03 07:46:56 +0000},
	date-modified = {2011-08-03 07:47:27 +0000},
	note = {arXiv:math/0310250 [math.QA]},
	title = {Ribbon Tableaux and the Heisenberg Algebra},
	year = {2003}}

@article{LamShimozono2007DualKacMoody,
	abstract = {Motivated by affine Schubert calculus, we construct a family of dual
	graded graphs $(\Gamma_s,\Gamma_w)$ for an arbitrary Kac-Moody algebra
	$\g(A)$. The graded graphs have the Weyl group $W$ of $\g(A)$ as
	vertex set and are labeled versions of the strong and weak orders
	of $W$ respectively. Using a construction of Lusztig for quivers
	with an admissible automorphism, we define folded insertion for a
	Kac-Moody algebra and obtain Sagan-Worley shifted insertion from
	Robinson-Schensted insertion as a special case. Drawing on work of
	Stembridge, we analyze the induced subgraphs of $(\Gamma_s,\Gamma_w)$
	which are distributive posets.},
	author = {Thomas Lam and Mark Shimozono},
	date-added = {2011-08-03 15:41:03 +0000},
	date-modified = {2011-08-03 15:41:34 +0000},
	eprint = {math/0702090v2},
	note = {arXiv:math/0702090 [math.CO]},
	title = {Dual graded graphs for Kac-Moody algebras},
	url = {http://arxiv.org/abs/math/0702090v2},
	bdsk-url-1 = {http://arxiv.org/abs/math/0702090v2}}

@article{lamperti1972semi,
	author = {Lamperti, J.},
	date-modified = {2018-02-28 19:39:25 +0000},
	journal = {Probab. Theory Relat. Fields},
	number = {3},
	pages = {205--225},
	publisher = {Springer},
	title = {{Semi-stable Markov processes. I}},
	volume = {22},
	year = {1972}}

@book{lando2003lectures,
	author = {Lando, S.K.},
	isbn = {0821834819},
	note = {Translated from Russian by the author},
	publisher = {Student Mathematical Library},
	title = {{Lectures on generating functions}},
	year = {2003}}

@book{lang1985sl2,
	author = {Lang, S.},
	isbn = {0387961984},
	publisher = {Springer},
	title = {{$SL_2(R)$}},
	year = {1985}}

@article{Lascoux2004OddStrict,
	author = {Lascoux, A.},
	date-added = {2011-08-03 07:26:06 +0000},
	date-modified = {2011-08-03 07:26:47 +0000},
	journal = {Discrete mathematics},
	number = {1-3},
	pages = {275-278},
	title = {Sylvester's bijection between strict and odd partitions},
	volume = {277},
	year = {2004}}

@article{Lascoux2009,
	abstract = {A one-parameter generalisation R_{\lambda}(X;b) of the symmetric Macdonald
	polynomials and interpolations Macdonald polynomials is studied from
	the point of view of branching rules. We establish a Pieri formula,
	evaluation symmetry, principal specialisation formula and q-difference
	equation for R_{\lambda}(X;b). We also prove a new multiple q-Gauss
	summation formula and several further results for sl_n basic hypergeometric
	series based on R_{\lambda}(X;b).},
	author = {Alain Lascoux and S. Ole Warnaar},
	comments = {28 pages},
	eprint = {0903.3996},
	oai2identifier = {0903.3996},
	owner = {leo},
	timestamp = {2009.04.13},
	title = {Branching rules for symmetric Macdonald polynomials and sl_n basic hypergeometric series},
	url = {http://arxiv.org/abs/0903.3996},
	year = {2009},
	bdsk-url-1 = {http://arxiv.org/abs/0903.3996}}

@article{Lassalle91a,
	author = {Lassalle, M.},
	date-added = {2011-09-11 11:59:00 +0000},
	date-modified = {2011-09-11 11:59:00 +0000},
	journal = {Comptes Rendus Acad. Sci., Paris, Ser. I},
	number = {6},
	pages = {425--428},
	title = {{Polyn\^omes de Jacobi g\'en\'eralis\'es}},
	volume = {312},
	year = {1991}}

@article{Lassalle91b,
	author = {Lassalle, M.},
	date-added = {2011-09-11 11:56:06 +0000},
	date-modified = {2011-09-11 12:00:02 +0000},
	journal = {Comptes Rendus Acad. Sci., Paris, Ser. I},
	number = {9},
	pages = {579-582},
	title = {{Polyn\^omes de Hermite g\'en\'eralis\'es}},
	volume = {312},
	year = {1991}}

@article{Lassalle91c,
	author = {Lassalle, M.},
	date-added = {2011-09-11 12:00:05 +0000},
	date-modified = {2011-09-11 12:00:24 +0000},
	journal = {Comptes Rendus Acad. Sci., Paris, Ser. I},
	number = {10},
	pages = {725-728},
	title = {{Polyn\^omes de Laguerre g\'en\'eralis\'es}},
	volume = {312},
	year = {1991}}

@article{Lassalle2006,
	abstract = {We give the explicit analytic development of Macdonald polynomials
	in terms of "modified complete" and elementary symmetric functions.
	These expansions are obtained by inverting the Pieri formula. Specialization
	yields similar developments for monomial, Jack and Hall-Littlewood
	symmetric functions.},
	author = {Michel Lassalle and Michael Schlosser},
	comments = {34 pages},
	eprint = {math/0402127},
	journal = {Adv. Math.},
	number = {2},
	oai2identifier = {math/0402127},
	owner = {leo},
	pages = {289-325},
	timestamp = {2009.04.13},
	title = {Inversion of the Pieri formula for Macdonald polynomials},
	url = {http://arxiv.org/abs/math/0402127},
	volume = {202},
	year = {2006},
	bdsk-url-1 = {http://arxiv.org/abs/math/0402127}}

@conference{DeFinetti,
	author = {Steffen Lauritzen},
	owner = {leo},
	timestamp = {2009.03.12},
	title = {Exchangeability and de Finetti's Theorem},
	year = {2007}}

@article{lenard1975states,
	author = {Lenard, A.},
	journal = {Archive for Rational Mechanics and Analysis},
	number = {3},
	pages = {219--239},
	publisher = {Springer},
	title = {{States of classical statistical mechanical systems of infinitely many particles. I}},
	volume = {59},
	year = {1975}}

@article{lenard1975statesII,
	author = {Lenard, A.},
	journal = {Archive for Rational Mechanics and Analysis},
	number = {3},
	pages = {241--256},
	publisher = {Springer},
	title = {{States of classical statistical mechanical systems of infinitely many particles. II. Characterization of correlation measures}},
	volume = {59},
	year = {1975}}

@article{lenard1973correlation,
	author = {Lenard, A.},
	date-modified = {2018-02-28 19:49:00 +0000},
	journal = {Comm. Math. Phys},
	number = {1},
	pages = {35--44},
	publisher = {Springer},
	title = {{Correlation functions and the uniqueness of the state in classical statistical mechanics}},
	volume = {30},
	year = {1973}}

@article{Li2010Glauber-Kawasaki,
	abstract = {We construct two types of equilibrium dynamics of an infinite particle
	system in a locally compact metric space $X$ for which a permanental
	point process is a symmetrizing, and hence invariant measure. The
	Glauber dynamics is a birth-and-death process in $X$, while in the
	Kawasaki dynamics interacting particles randomly hop over $X$. In
	the case $X=\mathbb R^d$, we consider a diffusion approximation for
	the Kawasaki dynamics at the level of Dirichlet forms. This leads
	us to an equilibrium dynamics of interacting Brownian particles for
	which a permanental point process is a symmetrizing measure.},
	author = {Guanhua Li and Eugene Lytvynov},
	eprint = {1005.4537},
	oai2identifier = {1005.4537},
	owner = {leo},
	timestamp = {2010.05.30},
	title = {A note on equilibrium Glauber and Kawasaki dynamics for permanental point processes},
	year = {2010}}

@article{Liang2009,
	author = {Liang, P. and Jordan, M.I. and Klein, D.},
	title = {{Probabilistic Grammars and Hierarchical Dirichlet Processes}},
	year = {2009}}

@article{Lieberman1972,
	author = {Lieberman, A.},
	date-added = {2011-06-15 15:17:52 +0400},
	date-modified = {2018-02-28 19:44:38 +0000},
	journal = {Trans. AMS},
	pages = {189-198},
	title = {The structure of certain unitary representations of infinite symmetric groups},
	volume = {164},
	year = {1972}}

@book{Liggett2010,
	address = {Providence, RI},
	author = {Liggett, T.},
	date-added = {2013-01-16 20:51:43 +0000},
	date-modified = {2013-01-16 20:52:41 +0000},
	publisher = {AMS},
	series = {Graduate Studies in Mathematics},
	title = {Continuous Time Markov Processes: An Introduction},
	volume = {113},
	year = {2010}}

@book{Liggett1999,
	author = {Liggett, T.},
	date-added = {2013-05-28 18:05:17 +0000},
	date-modified = {2013-05-28 18:06:41 +0000},
	publisher = {Springer},
	series = {{Grundlehren de mathematischen Wissenschaften}},
	title = {{Stochastic Interacting Systems: Contact, Voter and Exclusion Processes}},
	volume = {324},
	year = {1999}}

@book{Liggett1985,
	address = {Berlin},
	author = {Liggett, T.},
	date-added = {2013-05-28 18:04:25 +0000},
	date-modified = {2014-10-12 20:38:39 +0000},
	publisher = {Springer-Verlag},
	title = {{Interacting Particle Systems}},
	year = {2005}}

@article{lindstrom1973vector,
	author = {Lindstr{\"o}m, B.},
	date-added = {2012-11-04 22:00:49 +0000},
	date-modified = {2012-11-04 22:00:49 +0000},
	journal = {Bulletin of the London Mathematical Society},
	number = {1},
	pages = {85--90},
	publisher = {Oxford University Press},
	title = {On the vector representations of induced matroids},
	volume = {5},
	year = {1973}}

@electronic{Lisovyy2009,
	abstract = {We study a Fredholm determinant of the hypergeometric kernel arising
	in the representation theory of the infinite-dimensional unitary
	group. It is shown that this determinant coincides with the Palmer-Beatty-Tracy
	tau function of a Dirac operator on the hyperbolic disk. Solution
	of the connection problem for Painleve VI equation allows to determine
	its asymptotic behavior up to a constant factor, for which a conjectural
	expression is given in terms of Barnes functions. We also present
	analogous asymptotic results for the Whittaker and Macdonald kernel.},
	author = {O. Lisovyy},
	comments = {17 pages, 2 figures; v2: added references and derivation of Painleve VI from Tracy-Widom equations},
	eprint = {0910.1914},
	note = {arXiv:0910.1914 [math-ph]},
	oai2identifier = {0910.1914},
	owner = {leo},
	timestamp = {2009.11.26},
	title = {Dyson's constant for the hypergeometric kernel},
	year = {2009}}

@article{Littlewood1961,
	author = {Littlewood, D.E.},
	date-added = {2013-08-15 16:19:06 +0000},
	date-modified = {2013-08-15 16:19:42 +0000},
	journal = {Proc. London Math. Soc.},
	number = {485-498},
	title = {On certain symmetric functions},
	volume = {43},
	year = {1961}}

@article{logan_shepp1977variational,
	author = {Logan, BF and Shepp, L.A.},
	issn = {0001-8708},
	journal = {Adv. Math.},
	number = {2},
	pages = {206--222},
	publisher = {Elsevier},
	title = {{A variational problem for random Young tableaux}},
	volume = {26},
	year = {1977}}

@book{FOT94,
	author = {M. Fukushima, Y. Oshima and M. Takeda},
	owner = {leo},
	publisher = {Walter de Gruyter, Berlin/New York.},
	timestamp = {2010.04.22},
	title = {{Dirichlet Forms and Symmetric Markov Processes}},
	year = {1994}}

@book{ma1992introduction,
	author = {Ma, Z.M. and R{\"o}ckner, M.},
	publisher = {Universitext},
	title = {{Introduction to the theory of (non-symmetric) Dirichlet forms}},
	year = {1992}}

@book{Macdonald1995,
	author = {Macdonald, I.G.},
	edition = {2nd},
	owner = {leo},
	publisher = {Oxford University Press},
	timestamp = {2009.03.14},
	title = {Symmetric functions and {H}all polynomials},
	year = {1995}}

@unpublished{Macdonald87Hypergeometric,
	author = {Macdonald, I.G.},
	date-added = {2011-09-11 12:00:54 +0000},
	date-modified = {2011-09-11 12:02:23 +0000},
	note = {Unpublished manuscript},
	title = {Hypergeometric functions},
	year = {1987}}

@article{Maceachern1994,
	author = {MacEachern, SN and Muller, P.},
	institution = {Citeseer},
	title = {{Efficient estimation of mixture of Dirichlet process models}},
	year = {1994}}

@book{MacMahonBook,
	author = {MacMahon, P.A.},
	date-added = {2013-10-14 20:51:04 +0000},
	date-modified = {2013-10-14 20:51:51 +0000},
	note = {reprinted by Chelsea Publishing Company, New York, 1960},
	publisher = {Cambridge University Press},
	title = {{Combinatory Analysis}},
	year = {1915-1916}}

@article{MacMahon1912,
	author = {MacMahon, P.A.},
	date-added = {2013-10-14 20:27:43 +0000},
	date-modified = {2013-10-14 20:29:04 +0000},
	journal = {{Phil. Trans. Roy. Soc. London Ser. A}},
	pages = {345-373},
	title = {{Memoir on the Theory of the Partitions of Numbers. VI: Partitions in Two-Dimensional Space, to which is Added an Adumbration of the Theory of Partitions in Three-Dimensional Space}},
	volume = {211},
	year = {1912}}

@article{Mairesse2005,
	author = {Jean Mairesse},
	date-modified = {2018-02-28 19:49:30 +0000},
	journal = {Electron. J. Probab.},
	owner = {leo},
	pages = {1417-1441},
	timestamp = {2009.04.03},
	title = {Random Walks on Groups and Monoids with a Markovian Harmonic Measure},
	volume = {10},
	year = {2005}}

@book{Manin1984,
	address = {Moscow},
	author = {Manin, Yu.I},
	date-added = {2011-06-17 16:46:53 +0400},
	date-modified = {2018-04-14 04:20:11 +0000},
	publisher = {``Mir''},
	title = {Calibrated fields and complex geometry},
	year = {1984}}

@article{matsumoto2008jack,
	author = {Matsumoto, S.},
	date-modified = {2018-02-28 19:49:54 +0000},
	journal = {El. Jour. Combin.},
	note = {arXiv:0810.5619 [math.CO]},
	number = {R149},
	pages = {1},
	title = {{Jack deformations of Plancherel measures and traceless Gaussian random matrices}},
	volume = {15},
	year = {2008}}

@article{Matsumoto2005,
	abstract = {The shifted Schur measure introduced by Tracy and Widom is a measure
	on the set of all strict partitions, which is defined by Schur $Q$-functions.
	The main aim of this paper is to calculate the correlation function
	of this measure, which is given by a pfaffian. As an application,
	we prove that a limit distribution of $\lambda_j$'s with respect
	to a shifted version of the Plancherel measure for symmetric groups
	is identical with the corresponding distribution of the original
	Plancherel measure. Further we give expressions of the mean value
	and the variance of the size of a partition with respect to the measure
	defined by Hall-Littlewood functions.},
	author = {Matsumoto, S.},
	comments = {18 pages, the title of the first version is ``A limit distribution of the length of the longest ascent pair for a random permutation''},
	eprint = {math/0312373},
	journal = {J. Math. Soc. Japan, vol.},
	note = {arXiv:math/0312373 [math.CO]},
	number = {3},
	oai2identifier = {math/0312373},
	owner = {leo},
	pages = {619--637},
	timestamp = {2009.11.26},
	title = {{Correlation functions of the shifted Schur measure}},
	volume = {57},
	year = {2005}}

@article{matsumoto2005alpha,
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@article{matsumoto2005scaling,
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@article{mazza2002products,
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@article{MTW1977,
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	owner = {leo},
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	year = {1977}}

@article{Medem2001qPolynoms,
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	date-added = {2011-08-03 07:43:33 +0000},
	date-modified = {2011-08-03 07:44:09 +0000},
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@book{mehta2004random,
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@article{mehta1983some,
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@article{pandey1983gaussian,
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@article{MeliotCLT2011,
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	year = {2011}}

@article{Meliot20091/2,
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	date-added = {2013-05-15 20:40:50 +0000},
	date-modified = {2013-05-15 20:41:16 +0000},
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@article{Merker2010,
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	oai2identifier = {1003.3202},
	owner = {leo},
	timestamp = {2010.03.17},
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@article{Metcalfe2011GT,
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	of particles in $\{1,...,n\} \times \R$. For each $r \in \{1,...,n\}$,
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	pattern. A standard Gelfand-Tsetlin pattern has exactly $r$ particles
	on each level $r$, and particles on adjacent levels satisfy an interlacing
	constraint.},
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@book{Meyer1966,
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@article{Miller2008,
	abstract = {We conjecture a strong property for the up and down maps U and D in
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	over Z[t]. In particular, this would determine the integral structure
	of the maps U, D, UD, DU, including their ranks in any characteristic.
	As evidence, we prove the conjecture for the Young-Fibonacci lattice
	YF studied by Okada and its r-differential generalizations Z(r),
	as well as verifying many of its consequences for Young's lattice
	Y and the r-differential Cartesian products Y^r.},
	author = {Alexander Miller and Victor Reiner},
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	oai2identifier = {0811.1983},
	owner = {leo},
	timestamp = {2010.07.15},
	title = {Differential posets and Smith normal forms},
	year = {2008}}

@article{Molchanov1991,
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	pages = {139--282},
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	volume = {22},
	year = {1991}}

@book{Moran1962,
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	publisher = {Clarendon Press},
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	year = {1962}}

@article{MoriartyOConnell,
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	date-added = {2013-09-06 23:25:22 +0000},
	date-modified = {2013-09-06 23:27:08 +0000},
	note = {arXiv:math/0606296 [math.PR]},
	title = {{On the free energy of a directed polymer in a Brownian environment}},
	year = {2006}}

@article{Muller2004,
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	year = {2004}}

@article{Nagaev1987,
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	note = {Springer},
	owner = {leo},
	pages = {69-78},
	timestamp = {2009.08.14},
	title = {Properties of mode of spectral positive stable distributions},
	volume = {1233},
	year = {1987}}

@article{nagao2007pfaffian,
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	date-modified = {2018-02-28 19:41:34 +0000},
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	note = {arXiv:0708.2036 [math-ph]},
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	pages = {1137--1158},
	publisher = {Springer},
	title = {{Pfaffian Expressions for Random Matrix Correlation Functions}},
	volume = {129},
	year = {2007}}

@article{nagao1998multilevel,
	author = {Nagao, T. and Forrester, P.J.},
	journal = {Physics Letters A},
	number = {1-2},
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	publisher = {Elsevier},
	title = {{Multilevel dynamical correlation functions for Dyson's Brownian motion model of random matrices}},
	volume = {247},
	year = {1998}}

@article{nagao2003dynamical,
	author = {Nagao, T. and Katori, M. and Tanemura, H.},
	issn = {0375-9601},
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	note = {arXiv:cond-mat/0202068 [cond-mat.stat-mech]},
	number = {1},
	pages = {29--35},
	publisher = {Elsevier},
	title = {{Dynamical correlations among vicious random walkers}},
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	year = {2003}}

@article{NagaoWadati1991,
	author = {Nagao, T. and Wadati, M.},
	journal = {J. Phys. Soc. Japan},
	owner = {leo},
	pages = {3298-3322},
	timestamp = {2010.11.14},
	title = {{Correlation functions of random matrix ensembles related to classical orthogonal polynomials}},
	volume = {60},
	year = {1991}}

@article{NagaoWadati1992,
	author = {Nagao, T. and Wadati, M.},
	journal = {J. Phys. Soc. Japan},
	owner = {leo},
	pages = {78-88, 1910-1918},
	timestamp = {2010.11.14},
	title = {{Correlation functions of random matrix ensembles related to classical orthogonal polynomials II, III}},
	volume = {61},
	year = {1991}}

@article{Nazarov1992,
	author = {Nazarov, M.L.},
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	owner = {leo},
	pages = {115-130},
	timestamp = {2009.03.26},
	title = {Projective representations of the infinite symmetric group},
	volume = {9},
	year = {1992}}

@article{nazarov1992factor,
	author = {Nazarov, M.},
	date-modified = {2011-05-07 14:35:52 +0400},
	journal = {Journal of Mathematical Sciences},
	number = {2},
	pages = {2690--2698},
	publisher = {Springer},
	title = {{Factor representations of the infinite spin-symmetric group}},
	volume = {62},
	year = {1992}}

@article{Neal2000,
	author = {Neal, R.M.},
	journal = {Journal of computational and graphical statistics},
	pages = {249--265},
	publisher = {American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America},
	title = {{Markov chain sampling methods for Dirichlet process mixture models}},
	year = {2000}}

@article{nelson1959analytic,
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	pages = {572--615},
	title = {{Analytic vectors}},
	volume = {2},
	year = {1959}}

@article{Neretin2003BosonFermion,
	author = {Neretin, Yu.A.},
	date-added = {2011-08-03 07:57:30 +0000},
	date-modified = {2011-08-03 07:57:58 +0000},
	note = {arXiv:math-ph/0306077},
	title = {Structures of boson and fermion Fock spaces in the space of symmetric functions},
	year = {2003}}

@incollection{Neretin1988,
	address = {Moscow},
	author = {Neretin, Yu.A.},
	booktitle = {{Current Problems of Mathematics. Fundamental Directions}},
	date-added = {2011-06-15 11:49:47 +0400},
	date-modified = {2011-06-15 11:51:51 +0400},
	pages = {163-224},
	publisher = {VINITI},
	title = {{Representations of the Virasoro algebra and of affine algebras}},
	volume = {22},
	year = {1988}}

@article{Nessonov1986,
	author = {Nessonov, N.I.},
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	pages = {131-150},
	title = {{A complete classification of the representations of $GL(\infty)$ containing a unit representation of the unitary subgroup}},
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	year = {1986}}

@book{wilf1978combinatorial,
	author = {Nijenhuis, A. and Wilf, H.S.},
	publisher = {Academic Press New York},
	title = {{Combinatorial algorithms: for computers and calculators}},
	year = {1978}}

@book{nikiforov1991classical,
	author = {Nikiforov, A.F. and Suslov, S.K. and Uvarov, V.B.},
	date-added = {2012-11-08 15:54:54 +0000},
	date-modified = {2012-11-08 15:55:06 +0000},
	publisher = {Springer-Verlag Berlin},
	title = {Classical orthogonal polynomials of a discrete variable},
	year = {1991}}

@article{NordYoung2011,
	author = {Nordenstam, E. and Young, B.},
	date-added = {2012-02-03 02:32:01 +0000},
	date-modified = {2012-02-03 02:35:32 +0000},
	note = {arXiv:1201.4138 [math.CO]},
	title = {{Correlations for the Novak process}},
	year = {2012}}

@article{NordenstamYoung2011HalfHex,
	author = {Nordenstam, E. and Young, B.},
	date-added = {2011-08-03 06:56:31 +0000},
	date-modified = {2018-02-28 19:49:54 +0000},
	journal = {El. Jour. Combin.},
	note = {arXiv:1103.5054 [math.CO]},
	number = {1},
	pages = {P181},
	title = {{Domino shuffling on Novak half-hexagons and Aztec half-diamonds}},
	volume = {18},
	year = {2011}}

@incollection{NoumiYamada2004,
	address = {Tokyo},
	author = {Noumi, M. and Yamada, Y.},
	booktitle = {Representation theory of algebraic groups and quantum groups},
	date-added = {2013-05-03 03:21:55 +0000},
	date-modified = {2014-10-25 23:14:14 +0000},
	note = {arXiv:math-ph/0203030},
	pages = {371--442},
	publisher = {Math. Soc. Japan},
	series = {Adv. Stud. Pure Math.},
	title = {{Tropical Robinson-Schensted-Knuth correspondence and birational Weyl group actions}},
	volume = {40},
	year = {2004}}

@article{Oconnell2009_Toda,
	author = {O'Connell, N.},
	date-added = {2013-05-02 03:34:29 +0000},
	date-modified = {2013-05-02 03:35:21 +0000},
	journal = {Ann. Probab.},
	note = {arXiv:0910.0069 [math.PR]},
	number = {2},
	pages = {437-458},
	title = {{Directed polymers and the quantum Toda lattice}},
	volume = {40},
	year = {2012}}

@article{OConnell2003,
	author = {O'Connell, N.},
	date-added = {2013-02-07 17:51:15 +0000},
	date-modified = {2013-02-10 23:21:29 +0000},
	journal = {J. Phys. A},
	number = {12},
	pages = {3049-3066},
	title = {{Conditioned random walks and the RSK correspondence}},
	volume = {36},
	year = {2003}}

@article{OConnell2003Trans,
	author = {O'Connell, N.},
	date-added = {2013-04-08 05:53:10 +0000},
	date-modified = {2018-02-28 19:46:00 +0000},
	journal = {Trans. AMS},
	number = {9},
	pages = {3669-3697},
	title = {{A path-transformation for random walks and the Robinson-Schensted correspondence}},
	volume = {355},
	year = {2003}}

@article{OConnellPei2012,
	author = {O'Connell, N. and Pei, Y.},
	date-added = {2013-01-30 21:27:56 +0000},
	date-modified = {2018-02-28 19:50:15 +0000},
	journal = {Electron. J. Probab.},
	note = {arXiv:1212.6716 [math.CO]},
	number = {95},
	pages = {1-25},
	title = {{A q-weighted version of the Robinson-Schensted algorithm}},
	volume = {18},
	year = {2013}}

@article{OSZ2012,
	author = {O'Connell, N. and Sepp{\"a}l{\"a}inen, T. and Zygouras, N.},
	date-added = {2013-05-10 11:56:32 +0000},
	date-modified = {2014-10-15 01:46:12 +0000},
	journal = {Invent. Math.},
	note = {arXiv:1110.3489 [math.PR]},
	pages = {361-416},
	title = {{Geometric RSK correspondence, Whittaker functions and symmetrized random polymers}},
	volume = {197},
	year = {2014}}

@article{OConnellWarren2011,
	author = {O'Connell, N. and Warren, J.},
	date-added = {2013-05-11 01:10:29 +0000},
	date-modified = {2013-05-11 01:11:08 +0000},
	note = {arXiv:1104.3509 [math.PR]},
	title = {A multi-layer extension of the stochastic heat equation},
	year = {2011}}

@article{OConnellYor2001,
	author = {O'Connell, N. and Yor, M.},
	date-added = {2013-05-02 14:18:21 +0000},
	date-modified = {2013-05-02 14:18:56 +0000},
	journal = {Stochastic Processes and their Applications},
	number = {2},
	pages = {285-304},
	title = {{Brownian analogues of Burke's theorem}},
	volume = {96},
	year = {2001}}

@incollection{Okounkov2001a,
	author = {Okounkov, A.},
	booktitle = {Random matrix models and their applications},
	editor = {P.~M.~Bleher and A.~R.~Its},
	note = {arXiv:math/0002135 [math.RT]},
	owner = {leo},
	pages = {407--420},
	publisher = {Cambridge Univ. Press},
	series = {Mathematical Sciences Research Institute Publications},
	timestamp = {2009.03.26},
	title = {{SL(2) and z-measures}},
	volume = {40},
	year = {2001}}

@incollection{Okounkov2002,
	author = {Okounkov, A.},
	booktitle = {Symmetric functions 2001: Surveys of Developments and Perspectives},
	editor = {S. Fomin},
	note = {arXiv:math/0309074 [math.CO]},
	owner = {leo},
	publisher = {Kluwer Academic Publishers},
	timestamp = {2010.08.25},
	title = {Symmetric functions and random partitions},
	year = {2002}}

@electronic{okounkov2009noncommutative,
	author = {Okounkov, A.},
	date-added = {2012-10-29 04:32:26 +0000},
	date-modified = {2012-10-29 04:33:03 +0000},
	note = {arXiv:0907.2322 [math.AG]},
	title = {Noncommutative geometry of random surfaces},
	year = {2009}}

@article{okounkov2001infinite,
	author = {Okounkov, A.},
	journal = {Selecta Math.},
	note = {arXiv:math/9907127 [math.RT]},
	number = {1},
	pages = {57--81},
	publisher = {Springer},
	title = {{Infinite wedge and random partitions}},
	volume = {7},
	year = {2001}}

@article{okounkov2000random,
	author = {Okounkov, A.},
	date-modified = {2018-02-28 19:47:21 +0000},
	journal = {Int. Math. Res. Notices},
	note = {arXiv:math/9903176 [math.CO]},
	number = {20},
	pages = {1043--1095},
	title = {{Random matrices and random permutations}},
	volume = {2000},
	year = {2000}}

@article{Okounkov1997,
	author = {Andrei Okounkov},
	date-modified = {2012-11-03 05:05:26 +0000},
	journal = {Adv. Math.},
	number = {2},
	owner = {leo},
	pages = {258-282},
	timestamp = {2009.10.18},
	title = {{Log-Concavity of Multiplicities with Application to Characters of $U(\infty)$}},
	volume = {127},
	year = {1997}}

@article{Okounkov1996quantumImm,
	author = {Okounkov, A.},
	date-added = {2011-11-14 17:05:17 +0000},
	date-modified = {2011-11-14 17:06:49 +0000},
	doi = {10.1007/BF02587738},
	fjournal = {Transformation Groups},
	issn = {1083-4362},
	journal = {Transform. Groups},
	note = {arXiv:q-alg/9602028},
	number = {1-2},
	pages = {99--126},
	title = {Quantum immanants and higher {C}apelli identities},
	url = {http://dx.doi.org/10.1007/BF02587738},
	volume = {1},
	year = {1996},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=1390752},
	bdsk-url-2 = {http://dx.doi.org/10.1007/BF02587738}}

@incollection{OkOl2006BC,
	author = {Okounkov, A. and Olshanski, G.},
	booktitle = {Jack, Hall-Littlewood and Macdonald Polynomials. Contemporary Mathematics},
	date-added = {2012-10-21 23:56:46 +0000},
	date-modified = {2012-10-22 00:10:24 +0000},
	note = {arXiv:math/0606085 [math.RT]},
	pages = {281-318},
	publisher = {Amer. Math. Soc.},
	title = {{Limits of BC-type orthogonal polynomials as the number of variables goes to infinity}},
	volume = {417},
	year = {2006}}

@article{OkOl1998,
	author = {Okounkov, A. and Olshanski, G.},
	date-modified = {2011-11-14 17:21:06 +0000},
	journal = {Int. Math. Res. Notices},
	note = {arXiv:q-alg/9709011},
	number = {13},
	owner = {leo},
	pages = {641-682},
	timestamp = {2009.10.18},
	title = {{Asymptotics of Jack polynomials as the number of variables goes to infinity }},
	volume = {1998},
	year = {1998}}

@article{OkounkovOlshanski1996ShiftSchur,
	author = {Okounkov, A. and Olshanski, G.},
	date-added = {2011-11-14 17:15:32 +0000},
	date-modified = {2011-11-14 17:18:20 +0000},
	journal = {Algebra i Analiz},
	note = {translation in St. Petersburg Math. J. {\bf9} (1998), no. 2, 239---300, arXiv:q-alg/9605042},
	number = {2},
	pages = {73--146},
	title = {Shifted {S}chur functions},
	volume = {9},
	year = {1997}}

@article{OkounkovOlshanskiJack1996,
	author = {Okounkov, A. and Olshanski, G.},
	date-added = {2011-11-14 17:19:39 +0000},
	date-modified = {2011-11-14 17:20:33 +0000},
	fjournal = {Mathematical Research Letters},
	issn = {1073-2780},
	journal = {Math. Res. Lett.},
	note = {arXiv:q-alg/9608020},
	number = {1},
	pages = {69--78},
	title = {Shifted {J}ack polynomials, binomial formula, and applications},
	volume = {4},
	year = {1997},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=1432811}}

@article{Okounkov2005,
	abstract = {We study random skew 3D partitions weighted by $q^{\textup{vol}}$
	and, specifically, the $q\to 1$ asymptotics of local correlations
	near various points of the limit shape. We obtain sine-kernel asymptotics
	for correlations in the bulk of the disordered region, Airy kernel
	asymptotics near a general point of the frozen boundary, and a Pearcey
	kernel asymptotics near a cusp of the frozen boundary.},
	author = {Okounkov, A. and Reshetikhin, N.},
	date-modified = {2016-08-02 03:00:24 +0000},
	journal = {Commun. Math. Phys.},
	note = {arXiv:math/0503508 [math.CO]},
	number = {3},
	owner = {leo},
	pages = {571--609},
	title = {{Random skew plane partitions and the Pearcey process}},
	volume = {269},
	year = {2007},
	bdsk-url-1 = {http://arxiv.org/abs/math/0503508}}

@article{OkounkovReshetikhin2006RandomMatr,
	author = {Okounkov, A. and Reshetikhin, N.Y.},
	date-added = {2012-10-17 16:34:46 +0000},
	date-modified = {2012-10-17 16:35:20 +0000},
	journal = {Mosc. Math. J.},
	number = {3},
	pages = {553-566},
	title = {The birth of a~random matrix},
	volume = {6},
	year = {2006}}

@article{okounkov2003correlation,
	author = {Okounkov, A. and Reshetikhin, N.},
	date-modified = {2018-02-28 19:42:45 +0000},
	journal = {Jour. AMS},
	note = {arXiv:math/0107056 [math.CO]},
	number = {3},
	pages = {581--603},
	publisher = {American Mathematical Society},
	title = {{Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram}},
	volume = {16},
	year = {2003}}

@article{Vershik_Okounkov1996,
	author = {Okounkov, A. and Vershik, A.},
	date-added = {2011-05-07 13:16:16 +0400},
	date-modified = {2011-05-07 13:17:27 +0400},
	journal = {A new approach to representation theory of symmetric groups},
	number = {4},
	pages = {581--605},
	publisher = {Springer},
	title = {A new approach to representation theory of symmetric groups},
	volume = {2},
	year = {1996}}

@article{okura1998new,
	author = {Okura, H.},
	date-modified = {2011-03-23 11:47:06 +0300},
	journal = {Mem. Fac. Eng. and Design Kyoto Inst. Tech},
	pages = {1--12},
	title = {{A new approach to the skew product of symmetric Markov processes}},
	volume = {46},
	year = {1998}}

@incollection{Ollivier2010_survCRC,
	author = {Ollivier, Y.},
	booktitle = {Probabilistic approach to geometry},
	date-added = {2011-02-27 22:04:51 +0300},
	date-modified = {2011-02-27 22:08:08 +0300},
	publisher = {Mathematical Society of Japan},
	series = {Adv. Stud. Pure Math.},
	title = {A survey of Ricci curvature for metric spaces and Markov chains},
	volume = {57},
	year = {2010}}

@article{Ollivier2009_CRC,
	author = {Ollivier, Y.},
	date-added = {2011-02-27 22:06:38 +0300},
	date-modified = {2011-02-27 22:07:39 +0300},
	journal = {J. Funct. Anal.},
	number = {3},
	pages = {810-864},
	title = {Ricci curvature of Markov chains on metric spaces},
	volume = {256},
	year = {2009}}

@incollection{Olshanski1981_Symm_Tame_Semigroup,
	address = {Budapest},
	author = {Olshanski, G.},
	booktitle = {Representations of Lie groups and Lie algebras},
	date-added = {2011-05-22 12:05:35 +0200},
	date-modified = {2011-05-24 12:36:29 +0200},
	editor = {Kirillov, A.A.},
	pages = {181-197},
	publisher = {Akademiai Kiado},
	title = {Unitary representations of the infinite symmetric group: a semigroup approach},
	year = {1985}}

@article{Olshanski2011Meixner,
	author = {Olshanski, G.},
	date-added = {2011-07-06 16:41:28 +0400},
	date-modified = {2011-07-06 16:45:03 +0400},
	note = {arXiv:1103.5848 [math.CO]},
	title = {{Laguerre and Meixner orthogonal bases in the algebra of symmetric functions}},
	year = {2011}}

@article{Olshanski2009,
	abstract = {We construct a family of Markov processes with continuous sample trajectories
	on an infinite-dimensional space, the Thoma simplex. The family depends
	on three continuous parameters, one of which, the Jack parameter,
	is similar to the beta parameter in random matrix theory. The processes
	arise in a scaling limit transition from certain finite Markov chains,
	the so called up-down chains on the Young graph with the Jack edge
	multiplicities. Each of the limit Markov processes is ergodic and
	its stationary distribution is a symmetrizing measure. The infinitesimal
	generators of the processes are explicitly computed; viewed as selfadjoint
	operators in the L^2 spaces over the symmetrizing measures, the generators
	have purely discrete spectrum which is explicitly described. For
	the special value 1 of the Jack parameter, the limit Markov processes
	coincide with those of the recent work by Borodin and the author
	(Prob. Theory Rel. Fields 144 (2009), 281--318; arXiv:0810.3751).
	In the limit as the Jack parameter goes to 0, our family of processes
	degenerates to the one-parameter family of diffusions on the Kingman
	simplex studied long ago by Ethier and Kurtz in connection with some
	models of population genetics. The techniques of the paper are essentially
	algebraic. The main computations are performed in the algebra of
	shifted symmetric functions with the Jack parameter and rely on the
	concept of anisotropic Young diagrams due to Kerov.},
	author = {Olshanski, G.},
	comments = {AMS TeX, 53 pages, 1 figure},
	date-modified = {2018-02-28 19:47:21 +0000},
	eprint = {0902.3395},
	journal = {Int. Math. Res. Notices},
	note = {arXiv:0902.3395 [math.PR]},
	number = {6},
	oai2identifier = {0902.3395},
	owner = {leo},
	pages = {1102--1166},
	timestamp = {2009.03.11},
	title = {Anisotropic {Y}oung diagrams and infinite-dimensional diffusion processes with the {J}ack parameter},
	url = {http://arxiv.org/abs/0902.3395},
	volume = {2010},
	year = {2010},
	bdsk-url-1 = {http://arxiv.org/abs/0902.3395}}

@article{Olshanski2010LaguerreMeixner,
	author = {Olshanski, G.},
	date-added = {2011-11-14 17:09:51 +0000},
	date-modified = {2011-12-03 01:49:31 +0000},
	journal = {Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI)},
	note = {arXiv:1009.2037 [math.CO]},
	pages = {81--110, 230},
	title = {{Laguerre and Meixner symmetric functions, and infinite-dimensional diffusion processes}},
	volume = {378},
	year = {2010},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=2749298}}

@article{olshanski2010plancherel,
	author = {Olshanski, G.},
	date-modified = {2018-02-28 19:49:54 +0000},
	journal = {El. Jour. Combin.},
	note = {arXiv:0905.1304 [math.CO]},
	number = {R43},
	pages = {1},
	title = {{Plancherel averages: Remarks on a paper by Stanley}},
	volume = {17},
	year = {2010}}

@article{Olshanski2009a,
	abstract = {The Gamma kernel is a projection kernel of the form (A(x)B(y)-B(x)A(y))/(x-y),
	where A and B are certain functions on the one-dimensional lattice
	expressed through Euler's Gamma function. The Gamma kernel depends
	on two continuous parameters; its principal minors serve as the correlation
	functions of a determinantal probability measure P defined on the
	space of infinite point configurations on the lattice. As was shown
	earlier (Borodin and Olshanski, Advances in Math. 194 (2005), 141-202;
	arXiv:math-ph/0305043), P describes the asymptotics of certain ensembles
	of random partitions in a limit regime. Theorem: The determinantal
	measure P is quasi-invariant with respect to finitary permutations
	of the nodes of the lattice. This result is motivated by an application
	to a model of infinite particle stochastic dynamics.},
	author = {Olshanski, G.},
	comments = {53 pages, 2 figures; Version 2: minor corrections},
	eprint = {0910.0130},
	journal = {Adv. Math., to appear},
	note = {arXiv:0910.0130 [math.PR]},
	oai2identifier = {0910.0130},
	owner = {leo},
	timestamp = {2009.12.10},
	title = {{The quasi-invariance property for the Gamma kernel determinantal measure}},
	year = {2009}}

@article{Olshansk2008-difference,
	author = {Olshanski, G.},
	date-added = {2011-03-23 11:40:34 +0300},
	date-modified = {2011-03-23 11:46:39 +0300},
	journal = {Functional Analysis and Its Applications},
	note = {arXiv:0810.3751 [math.PR]},
	number = {4},
	pages = {317-329},
	title = {Difference operators and determinantal point processes},
	volume = {42},
	year = {2008}}

@unpublished{Olshanski-fockone,
	author = {Olshanski, G.},
	note = {unpublished work},
	owner = {leo},
	timestamp = {2010.08.13},
	title = {{Fock Space and Time-dependent Determinantal Point Processes}},
	year = {2008}}

@article{Olshanski2003,
	abstract = {The goal of harmonic analysis on a (noncommutative) group is to decompose
	the most `natural' unitary representations of this group (like the
	regular representation) on irreducible ones. The infinite-dimensional
	unitary group U(infinity) is one of the basic examples of `big' groups
	whose irreducible representations depend on infinitely many parameters.
	Our aim is to explain what the harmonic analysis on U(infinity) consists
	of. We deal with unitary representations of a reasonable class, which
	are in 1-1 correspondence with characters (central, positive definite,
	normalized functions on U(infinity)). The decomposition of any representation
	of this class is described by a probability measure (called spectral
	measure) on the space of indecomposable characters. The indecomposable
	characters were found by Dan Voiculescu in 1976. The main result
	of the present paper consists in explicitly constructing a 4-parameter
	family of `natural' representations and computing their characters.
	We view these representations as a substitute of the nonexisting
	regular representation of U(infinity). We state the problem of harmonic
	analysis on U(infinity) as the problem of computing the spectral
	measures for these `natural' representations. A solution to this
	problem is given in the next paper math/0109194, joint with Alexei
	Borodin. We also prove a few auxiliary general results. In particular,
	it is proved that the spectral measure of any character of U(infinity)
	can be approximated by a sequence of (discrete) spectral measures
	for the restrictions of the character to the compact unitary groups
	U(N). This fact is a starting point for computing spectral measures.},
	author = {Grigori Olshanski},
	comments = {AMSTeX, 50 pages},
	eprint = {math/0109193},
	journal = {J. Funct. Anal.},
	number = {2},
	oai2identifier = {math/0109193},
	owner = {leo},
	pages = {464-524},
	timestamp = {2009.05.18},
	title = {The problem of harmonic analysis on the infinite-dimensional unitary group},
	volume = {205},
	year = {2003}}

@electronic{Olshanski1998,
	abstract = {The matrix Whittaker kernel has been introduced by A. Borodin in Part
	IV of the present series of papers. This kernel describes a point
	process -- a probability measure on a space of countable point configurations.
	The kernel is expressed in terms of the Whittaker confluent hypergeometric
	functions. It depends on two parameters and determines a $J$-symmetric
	operator $K$ in $L^2(R_+)\oplus L^2(R_+)$. It turns out that the
	operator $K$ can be represented in the form $L(1+L)^{-1}$, where
	$L$ is a rather simple integral operator: the kernel of $L$ is expressed
	in terms of elementary functions only. This is our main result; it
	elucidates the nature of the matrix Whittaker kernel and makes it
	possible to directly verify the existence of the associated point
	process. Next, we show that the matrix Whittaker kernel can be degenerated
	to a family of kernels expressed through the Bessel and Macdonald
	functions. In this way one can obtain both the well-known Bessel
	kernel (which arises in random matrix theory) and certain interesting
	new kernels.},
	author = {Olshanski, G.},
	comments = {AMSTeX, 25 pages},
	eprint = {math/9810014},
	note = {arXiv:math/9810014},
	oai2identifier = {math/9810014},
	owner = {leo},
	timestamp = {2009.11.17},
	title = {{Point processes and the infinite symmetric group. Part V: Analysis of the matrix Whittaker kernel}},
	year = {1998}}

@article{Olshanski1989_GK_Symm_eng,
	author = {Olshanski, G.},
	date-added = {2011-05-22 12:01:04 +0200},
	date-modified = {2011-05-22 12:09:37 +0200},
	journal = {Leningr. Math. J.},
	note = {in Russian: Algebra Anal. 1, no. 4, 178-209 (1989)},
	number = {4},
	pages = {983-1014},
	title = {{Unitary representations of $(G,K)$-pairs connected with the infinite symmetric group $S(\infty)$}},
	volume = {1},
	year = {1990}}

@article{Olshanski1989_GK_rus,
	author = {Olshanski, G.},
	date-added = {2011-04-22 08:45:50 +0400},
	date-modified = {2011-05-22 12:09:26 +0200},
	journal = {Algebra i Analiz},
	note = {English translation: Leningrad Math. J. 1 (1990), 983--1014},
	number = {4},
	pages = {178-209 (in Russian)},
	title = {Unitary representations of $(G,K)$-pairs connected with the infinite symmetric group $S(\infty)$},
	volume = {1},
	year = {1989}}

@article{Olshanski1988,
	author = {Olshanski, G.},
	date-added = {2011-06-15 11:37:11 +0400},
	date-modified = {2011-06-15 11:38:09 +0400},
	journal = {Functional Analysis and Its Applications},
	number = {4},
	pages = {273-285},
	title = {{Method of holomorphic extensions in the theory of unitary representations of infinite-dimensional classical groups}},
	volume = {22},
	year = {1988}}

@article{Olshanski1988Extension,
	author = {Olshanski, G.},
	date-added = {2011-06-15 12:46:13 +0400},
	date-modified = {2011-06-15 12:48:21 +0400},
	journal = {Doklady AN SSSR},
	number = {5},
	pages = {1050-1054},
	title = {{Extension of the algebra U(g) for infinite-dimensional classical Lie algebras g and the Yangians Y(gl(m))}},
	volume = {297},
	year = {1988}}

@article{Olshanski1986,
	author = {Olshanski, G.},
	date-added = {2011-06-15 11:33:46 +0400},
	date-modified = {2011-06-15 11:37:08 +0400},
	journal = {Functional Analysis and Its Applications},
	number = {4},
	pages = {292-301},
	title = {{Unitary representations of the group $SO(\infty,\infty)$ as limits of unitary representations of the groups $SO(n,\infty)$ as $n\to\infty$}},
	volume = {20},
	year = {1987}}

@article{Olshanski1984,
	author = {Olshanski, G.},
	date-added = {2011-06-15 11:32:10 +0400},
	date-modified = {2011-06-15 11:32:49 +0400},
	journal = {Functional Analysis and Its Applications},
	number = {1},
	pages = {22-34},
	title = {{Infinite-dimensional classical groups of finite R-rank: description of representations and asymptotic theory}},
	volume = {18},
	year = {1984}}

@article{Olshanski1983,
	author = {Olshanski, G.},
	date-added = {2011-06-15 11:28:48 +0400},
	date-modified = {2011-06-15 11:31:21 +0400},
	journal = {Doklady AN SSSR},
	number = {1},
	pages = {33-36},
	title = {{Unitary representations of infinite-dimensional pairs $(G, K)$ and the formalism of R. Howe}},
	volume = {269},
	year = {1983}}

@incollection{Olshanski1980TypeI,
	address = {Moscow},
	author = {Olshanski, G.},
	booktitle = {{Current Problems of Mathematics}},
	date-added = {2011-06-15 15:18:43 +0400},
	date-modified = {2011-06-15 15:21:01 +0400},
	pages = {31-52},
	publisher = {VINITI},
	title = {{New `large' groups of type I}},
	volume = {16},
	year = {1980}}

@article{Olshanski1978,
	author = {Olshanski, G.},
	date-added = {2011-06-15 11:26:00 +0400},
	date-modified = {2011-06-15 11:28:25 +0400},
	journal = {Functional Analysis and Its Applications},
	number = {3},
	pages = {185--195},
	title = {{Unitary representations of the infinite-dimensional classical groups $U(p,\infty)$, $SO(p,\infty)$, $Sp(p,\infty)$ and the corresponding motion groups}},
	volume = {12},
	year = {1978}}

@incollection{OlshRegVer2003,
	author = {Olshanski, G. and Regev, A. and Vershik, A.},
	booktitle = {{Studies in Memory of Issai Schur}},
	editor = {Joseph, A. and Melnikov, A. and Rentschler, R.},
	note = {arXiv:math/0110077 [math.CO]},
	owner = {leo},
	pages = {251--300},
	publisher = {Birkhauser},
	series = {Progress in Mathematics},
	timestamp = {2010.11.17},
	title = {{Frobenius--Schur functions}},
	volume = {210},
	year = {2003}}

@incollection{OlVer1996,
	author = {G. Olshanski and A. Vershik},
	booktitle = {Contemporary Mathematical Physics. F.A..Berezi's memorial volume. American Mathematical Society Translations, (Advances in the Mathematical Sciences --- 31)},
	date-modified = {2020-07-07 10:28:34 -0400},
	note = {arXiv:math/9601215v1 [math.RT]},
	owner = {leo},
	pages = {137-175},
	publisher = {AMS},
	series = {2},
	timestamp = {2010.04.25},
	title = {{Ergodic unitarily invariant measures on the space of infinite Hermitian matrices}},
	volume = {175},
	year = {1996}}

@article{overbeck1997geometric,
	author = {OVERBECK, L. and R{\\"O}CKNER, M.},
	journal = {Random Operators and Stochastic Equations},
	number = {1},
	pages = {35--58},
	publisher = {Walter de Gruyter, Berlin/New York Berlin, New York},
	title = {{Geometric aspects of finite and infinite-dimensional Fleming-Viot processes}},
	volume = {5},
	year = {1997}}

@article{overbeck1995analytic,
	author = {Overbeck, L. and Schmuland, B.},
	date-modified = {2018-02-28 19:46:40 +0000},
	journal = {Ann. Probab.},
	number = {1},
	pages = {1--36},
	publisher = {Institute of Mathematical Statistics},
	title = {{An analytic approach to Fleming-Viot processes with interactive selection}},
	volume = {23},
	year = {1995}}

@article{Ovsienko2009Pentagram,
	author = {Valentin Ovsienko and Richard Schwartz and Serge Tabachnikov},
	date-added = {2012-09-23 13:46:32 +0000},
	date-modified = {2012-09-23 13:46:47 +0000},
	title = {The Pentagram map: a discrete integrable system},
	year = {2008},
	bdsk-url-1 = {http://arxiv.org/abs/0810.5605}}

@article{Peccati2008DirichletProcess,
	author = {Peccati, G.},
	date-added = {2011-08-03 08:13:34 +0000},
	date-modified = {2011-08-03 08:14:17 +0000},
	note = {arXiv:0803.1029 [math.ST]},
	title = {Multiple integral representation for functionals of Dirichlet processes},
	year = {2008}}

@article{Pei2013Symmetry,
	author = {Pei, Y.},
	date-modified = {2015-03-12 12:29:57 +0000},
	eprint = {1306.2208},
	journal = {J. Algebr. Comb.},
	note = {arXiv:1306.2208 [math.CO]},
	owner = {leo},
	pages = {743-770},
	timestamp = {2013.07.21},
	title = {{A symmetry property for q-weighted Robinson-Schensted algorithms and other branching insertion algorithms}},
	volume = {40},
	year = {2013}}

@article{Pemantle2009,
	abstract = {Given a barrier $0 \leq b_0 \leq b_1 \leq ...$, let $f(n)$ be the
	number of nondecreasing integer sequences $0 \leq a_0 \leq a_1 \leq
	... \leq a_n$ for which $a_j \leq b_j$ for all $0 \leq j \leq n$.
	Known formul\ae for $f(n)$ include an $n \times n$ determinant whose
	entries are binomial coefficients (Kreweras, 1965) and, in the special
	case of $b_j = rj+s$, a short explicit formula (Proctor, 1988, p.320).
	A relatively easy bivariate recursion, decomposing all sequences
	according to $n$ and $a_n$, leads to a bivariate generating function,
	then a univariate generating function, then a linear recursion for
	$\{f(n) \}$. Moreover, the coefficients of the bivariate generating
	function have a probabilistic interpretation, leading to an analytic
	inequality which is an identity for certain values of its argument.},
	author = {Robin Pemantle and Herbert S. Wilf},
	eprint = {0905.0609},
	oai2identifier = {0905.0609},
	owner = {leo},
	timestamp = {2009.05.20},
	title = {Counting nondecreasing integer sequences that lie below a barrier},
	year = {2009}}

@article{perman1992size,
	author = {Perman, M. and Pitman, J. and Yor, M.},
	date-modified = {2018-02-28 19:39:25 +0000},
	journal = {Probab. Theory Relat. Fields},
	number = {1},
	pages = {21--39},
	publisher = {Springer},
	title = {{Size-biased sampling of Poisson point processes and excursions}},
	volume = {92},
	year = {1992}}

@article{Petersen2005,
	abstract = {We develop a more general view of Stembridge's enriched $P$-partitions
	and use this theory to outline the structure of peak algebras for
	the symmetric group and the hyperoctahedral group. Initially we focus
	on commutative peak algebras, spanned by sums of permutations with
	the same number of peaks, where we consider several variations on
	the definition of "peak." Whereas Stembridge's enriched $P$-partitions
	are related to quasisymmetric functions (the dual coalgebra of Solomon's
	type A descent algebra), our generalized enriched $P$-partitions
	are related to type B quasisymmetric functions (the dual coalgebra
	of Solomon's type B descent algebra). Using these functions, we move
	on to explore (non-commutative) peak algebras spanned by sums of
	permutations with the same set of peaks. While some of these algebras
	have been studied before, our approach gives explicit structure constants
	with a combinatorial description.},
	author = {T. Kyle Petersen},
	comments = {39 pages, 8 figures},
	eprint = {math/0508041},
	oai2identifier = {math/0508041},
	owner = {leo},
	timestamp = {2009.03.12},
	title = {Enriched $P$-partitions and peak algebras},
	url = {http://arxiv.org/abs/math/0508041},
	year = {2005},
	bdsk-url-1 = {http://arxiv.org/abs/math/0508041}}

@article{Petrov2011sl2,
	author = {Petrov, L.},
	date-added = {2011-12-14 22:40:51 +0000},
	date-modified = {2018-04-15 18:00:37 +0000},
	eprint = {1111.3399},
	journal = {J. Algebr. Comb.},
	note = {arXiv:1111.3399 [math.CO]},
	number = {3},
	pages = {663-720},
	title = {$\mathfrak{sl(2)}$ Operators and Markov Processes on Branching Graphs},
	volume = {38},
	year = {2013}}

@article{Petrov2012,
	author = {Petrov, L.},
	date-added = {2012-02-26 13:36:10 +0000},
	date-modified = {2018-02-28 19:38:39 +0000},
	eprint = {1202.3901},
	journal = {Probab. Theory Relat. Fields},
	note = {arXiv:1202.3901 [math.PR]},
	number = {3},
	pages = {429-487},
	title = {{Asymptotics of Random Lozenge Tilings via Gelfand-Tsetlin Schemes}},
	volume = {160},
	year = {2014}}

@article{Petrov2012GFF,
	author = {Petrov, L.},
	date-added = {2012-06-29 15:20:17 +0000},
	date-modified = {2016-05-04 16:39:09 +0000},
	eprint = {1206.5123},
	journal = {{Ann. Probab.}},
	note = {arXiv:1206.5123 [math.PR].},
	number = {1},
	pages = {1-43},
	title = {{Asymptotics of Uniformly Random Lozenge Tilings of Polygons. Gaussian Free Field}},
	volume = {43},
	year = {2015}}

@article{Petrov2012GT,
	author = {Petrov, L.},
	date-added = {2012-09-28 00:01:10 +0000},
	date-modified = {2014-10-08 19:46:17 +0000},
	eprint = {1208.3443},
	journal = {Mosc. Math. J.},
	note = {arXiv:1208.3443 [math.CO]},
	number = {1},
	pages = {121-160},
	title = {{The Boundary of the Gelfand-Tsetlin Graph: New Proof of Borodin-Olshanski's Formula, and its q-analogue}},
	volume = {14},
	year = {2014}}

@article{Petrov2010Pfaffian,
	author = {Petrov, L.},
	date-modified = {2018-02-28 19:50:15 +0000},
	eprint = {1011.3329},
	journal = {Electron. J. Probab.},
	note = {arXiv:1011.3329 [math.PR]},
	owner = {leo},
	pages = {2246-2295},
	timestamp = {2010.09.27},
	title = {Pfaffian stochastic dynamics of strict partitions},
	volume = {16},
	year = {2011}}

@conference{Petrov2011z,
	author = {Petrov, L.},
	booktitle = {Proceedings of the international conference ``50 years of IITP''},
	date-added = {2011-12-14 22:04:28 +0000},
	date-modified = {2011-12-14 22:41:38 +0000},
	eprint = {1107.0676},
	note = {arXiv:1107.0676 [math.CO]},
	title = {{On Measures on Partitions Arising in Harmonic Analysis for Linear and Projective Characters of the Infinite Symmetric Group}},
	year = {2011}}

@article{petrov2009eng,
	author = {Petrov, L.},
	eprint = {0904.1823},
	journal = {Jour. Math. Sci.},
	note = {in Russian: Zap. Nauchn. Sem. POMI {\bf{}373\/} (2009), 226--272, arXiv:0904.1823 [math.PR]},
	number = {3},
	pages = {437--463},
	publisher = {Springer},
	title = {{Random walks on strict partitions}},
	volume = {168},
	year = {2010}}

@article{Petrov2010,
	author = {Petrov, L.},
	date-modified = {2018-02-28 19:49:16 +0000},
	eprint = {1002.2714},
	journal = {Electron. Commun. Probab.},
	note = {arXiv:1002.2714 [math.PR]},
	owner = {leo},
	pages = {162-175},
	timestamp = {2010.07.02},
	title = {{Random Strict Partitions and Determinantal Point Processes}},
	volume = {15},
	year = {2010}}

@article{Petrov2007,
	abstract = {The aim of the paper is to introduce a two-parameter family of infinite-dimensional
	diffusion processes X(alpha,theta) related to Pitman's two-parameter
	Poisson-Dirichlet distributions PD(alpha,theta). The diffusions X(alpha,theta)
	are obtained in a scaling limit transition from certain finite Markov
	chains on partitions of natural numbers. The state space of X(alpha,theta)
	is an infinite-dimensional simplex called the Kingman simplex. In
	the special case when parameter alpha vanishes, our finite Markov
	chains are similar to Moran-type model in population genetics, and
	our diffusion processes reduce to the infinitely-many-neutral-alleles
	diffusion model studied by Ethier and Kurtz (1981). Our main results
	extend those of Ethier and Kurtz to the two-parameter case and are
	as follows: The Poisson-Dirichlet distribution PD(alpha,theta) is
	a unique stationary distribution for the corresponding process X(alpha,theta);
	the process is ergodic and reversible; the spectrum of its generator
	is explicitly described. The general two-parameter case seems to
	fall outside the setting of models of population genetics, and our
	approach differs in some aspects from that of Ethier and Kurtz. We
	also consider the case of degenerate series of parameters alpha and
	theta and conclude that the diffusions in finite-dimensional simplexes
	studied by Ethier and Kurtz (1981) arise as a special case of our
	two-parameter family of diffusions.},
	author = {Petrov, L.},
	comments = {LaTex, 20 pages; v2: minor typos fixed, v3: title changed, discussion clarified and improved (conclusions unchanged), added new results about degenerate series of parameters},
	eprint = {0708.1930},
	journal = {Functional Analysis and Its Applications},
	note = {arXiv:0708.1930 [math.PR]},
	number = {4},
	oai2identifier = {0708.1930},
	owner = {leo},
	pages = {279-296},
	timestamp = {2009.03.11},
	title = {A two-parameter family of infinite-dimensional diffusions in the {K}ingman simplex},
	volume = {43},
	year = {2009},
	bdsk-url-1 = {http://arxiv.org/abs/0708.1930}}

@article{Petrov2009umn_eng,
	author = {Petrov, L.},
	doi = {10.1070/RM2009v064n06ABEH004658},
	journal = {Russian Mathematical Surveys},
	number = {6},
	owner = {leo},
	pages = {1139--1141},
	timestamp = {2010.10.24},
	title = {Limit behaviour of certain random walks on strict partitions},
	url = {http://iopscience.iop.org/article/10.1070/RM2009v064n06ABEH004658/meta},
	volume = {64},
	year = {2009},
	bdsk-url-1 = {http://iopscience.iop.org/article/10.1070/RM2009v064n06ABEH004658/meta},
	bdsk-url-2 = {https://doi.org/10.1070/RM2009v064n06ABEH004658}}

@book{Phelps66,
	author = {Phelps, R.R.},
	date-added = {2012-09-11 23:18:03 +0000},
	date-modified = {2012-09-11 23:18:41 +0000},
	publisher = {Van Nostrand},
	title = {{Lectures on Choquet's theorems}},
	year = {1966}}

@book{Pitman2002,
	address = {Berlin},
	author = {Jim Pitman},
	citeseercitationcount = {0},
	citeseerurl = {http://citeseer.ist.psu.edu/610513.html},
	note = {http://works.bepress.com/jim\_pitman/1},
	owner = {leo},
	publisher = {Springer-Verlag},
	series = {Lect. Notes in Math. 1875},
	timestamp = {2009.03.11},
	title = {Combinatorial Stochastic Processes: Ecole d'Et{\'e} de Probabilit{\'e}s de Saint-Flour XXXII - 2002},
	year = {2006},
	bdsk-url-1 = {http://citeseer.ist.psu.edu/610513.html}}

@article{Pitman1996,
	author = {Jim Pitman},
	journal = {Statistics, Probability and Game Theory},
	owner = {leo},
	timestamp = {2010.01.09},
	title = {{Some Developments of the Blackwell-MacQueen Urn Scheme}},
	year = {1996}}

@article{pitman1996random,
	author = {Pitman, J.},
	journal = {Advances in Applied Probability},
	number = {2},
	pages = {525--539},
	publisher = {Applied Probability Trust},
	title = {{Random discrete distributions invariant under size-biased permutation}},
	volume = {28},
	year = {1996}}

@article{Pitman1995,
	author = {Jim Pitman},
	date-modified = {2018-02-28 19:39:09 +0000},
	journal = {Probab. Theory Relat. Fields},
	mrclass = {60G09 (60C05)},
	mrnumber = {MR1337249},
	pages = {145-158},
	title = {Exchangeable and partially exchangeable random partitions},
	volume = {102},
	year = {1995},
	znumber = {0821.60047}}

@techreport{Pitman1992,
	author = {J. Pitman},
	institution = {Dept. Statistics, U. C. Berkeley},
	note = {http://www.stat.berkeley.edu/tech-reports/},
	number = {345},
	owner = {leo},
	timestamp = {2009.03.27},
	title = {The two-parameter generalization of {E}wens' random partition structure},
	type = {Technical report},
	year = {1992}}

@article{Pitman2008,
	abstract = {We use a natural ordered extension of the Chinese Restaurant Process
	to grow a two-parameter family of binary self-similar continuum fragmentation
	trees. We provide an explicit embedding of Ford's sequence of alpha
	model trees in the continuum tree which we identified in a previous
	article as a distributional scaling limit of Ford's trees. In general,
	the Markov branching trees induced by the two-parameter growth rule
	are not sampling consistent, so the existence of compact limiting
	trees cannot be deduced from previous work on the sampling consistent
	case. We develop here a new approach to establish such limits, based
	on regenerative interval partitions and the urn-model description
	of sampling from Dirichlet random distributions.},
	author = {Jim Pitman and Matthias Winkel},
	comments = {33 pages, 4 figures},
	eprint = {0803.3098},
	oai2identifier = {0803.3098},
	owner = {leo},
	timestamp = {2009.08.09},
	title = {Regenerative tree growth: binary self-similar continuum random trees and Poisson-Dirichlet compositions},
	year = {2008}}

@article{Pitman1997,
	author = {Pitman, J. and Yor, M.},
	date-modified = {2016-05-04 16:38:35 +0000},
	journal = {{Ann. Probab.}},
	number = {2},
	owner = {leo},
	pages = {855-900},
	timestamp = {2009.08.09},
	title = {Two-parameter {P}oisson-{D}irichlet distribution derived from a stable subordinator},
	volume = {25},
	year = {1997}}

@article{pittel2007limit,
	author = {Pittel, B. and Romik, D.},
	issn = {0196-8858},
	journal = {Advances in Applied Mathematics},
	number = {2},
	pages = {164--209},
	publisher = {Elsevier},
	title = {{Limit shapes for random square Young tableaux}},
	volume = {38},
	year = {2007}}

@article{pittel2004limit,
	author = {Pittel, B. and Romik, D.},
	journal = {Arxiv preprint math/0405190},
	title = {{Limit shapes for random square Young tableaux and plane partitions}},
	year = {2004}}

@article{Povolotsky2013,
	author = {Povolotsky, A.},
	date-added = {2013-08-12 11:52:09 +0000},
	date-modified = {2015-03-19 16:47:11 +0000},
	journal = {J. Phys. A},
	note = {arXiv:1308.3250 [math-ph]},
	pages = {465205},
	title = {{On integrability of zero-range chipping models with factorized steady state}},
	volume = {46},
	year = {2013}}

@article{PovolotskyPriezzhev2006,
	author = {Povolotsky, A. and Priezzhev, V.},
	journal = {Journal of Statistical Mechanics: Theory and Experiment},
	note = {arXiv:cond-mat/0605150 [cond-mat.stat-mech]},
	pages = {P07002},
	title = {Determinant solution for the totally asymmetric exclusion process with parallel update},
	volume = {2006},
	year = {2006}}

@article{Povolotsky_Mendes_2006,
	author = {Povolotsky, A. and Mendes, J.F.F.},
	date-added = {2013-08-12 11:53:50 +0000},
	date-modified = {2018-02-28 19:41:34 +0000},
	journal = {J. Stat. Phys},
	note = {arXiv:cond-mat/0411558 [cond-mat.stat-mech]},
	number = {1},
	pages = {125-166},
	title = {{Bethe ansatz solution of discrete time stochastic processes with fully parallel update}},
	volume = {123},
	year = {2006}}

@article{Proctor1984Bruhat,
	author = {Proctor, R.A.},
	date-added = {2011-11-08 16:58:08 +0000},
	date-modified = {2011-11-14 17:24:04 +0000},
	fjournal = {European Journal of Combinatorics},
	issn = {0195-6698},
	journal = {European J. Combin.},
	number = {4},
	pages = {331--350},
	title = {Bruhat lattices, plane partition generating functions, and minuscule representations},
	volume = {5},
	year = {1984},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=782055}}

@article{Proctor1982sl2posets,
	author = {Proctor, R.A.},
	date-added = {2011-10-03 16:02:55 +0000},
	date-modified = {2011-10-03 16:03:35 +0000},
	journal = {SIAM J. Algebraic Discrete Methods},
	number = {2},
	pages = {275-280},
	title = {Representations of sl(2,C) on posets and the Sperner property},
	volume = {3},
	year = {1982}}

@article{proctor1982solution,
	author = {Proctor, R.A.},
	date-added = {2011-09-28 15:13:53 +0000},
	date-modified = {2011-09-28 15:13:53 +0000},
	journal = {The American Mathematical Monthly},
	number = {10},
	pages = {721--734},
	publisher = {JSTOR},
	title = {Solution of two difficult combinatorial problems with linear algebra},
	volume = {89},
	year = {1982}}

@article{Proctor1990PP,
	author = {Proctor, Robert A.},
	coden = {JCBTA7},
	date-added = {2011-11-08 16:54:51 +0000},
	date-modified = {2011-11-08 16:55:04 +0000},
	doi = {10.1016/0097-3165(90)90032-R},
	fjournal = {Journal of Combinatorial Theory. Series A},
	issn = {0097-3165},
	journal = {J. Combin. Theory Ser. A},
	mrclass = {05E25 (05A18 05E15 06A07)},
	mrnumber = {1059997 (91g:05137)},
	mrreviewer = {John R. Stembridge},
	number = {2},
	pages = {225--234},
	title = {Solution of a {S}perner conjecture of {S}tanley with a construction of {G}el\cprime fand},
	url = {http://dx.doi.org/10.1016/0097-3165(90)90032-R},
	volume = {54},
	year = {1990},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=1059997},
	bdsk-url-2 = {http://dx.doi.org/10.1016/0097-3165(90)90032-R}}

@article{1983,
	abstract = {The number of shifted plane partitions contained in the shifted shape
	[ p + q - 1, p + q - 3,..., p - q + 1 ] with part size bounded by
	m is shown to be equal to the number of ordinary plane partitions
	contained in the shape (p, p,..., p) (q rows) with part size bounded
	by m. The proof uses known combinatorial descriptions of finite-dimensional
	representations of semisimple Lie algebras. A separate simpler argument
	shows that the number of chains of cardinality k in the poset underlying
	the shifted plane partitions is equal to the number of chains of
	cardinality k in the poset underlying the ordinary plane partitions.
	The first result can also be formulated as an equality of chain counts
	for a pair of posets. The pair of posets is obtained by taking order
	ideals in the other pair of posets.},
	author = {Proctor, Robert A.},
	copyright = {Copyright {\copyright} 1983 American Mathematical Society},
	date-added = {2011-11-07 13:46:20 +0000},
	date-modified = {2011-11-07 13:46:20 +0000},
	issn = {00029939},
	journal = {Proceedings of the American Mathematical Society},
	jstor_articletype = {research-article},
	jstor_formatteddate = {Nov., 1983},
	language = {English},
	number = {3},
	pages = {pp. 553-559},
	publisher = {American Mathematical Society},
	title = {Shifted Plane Partitions of Trapezoidal Shape},
	url = {http://www.jstor.org/stable/2045516},
	volume = {89},
	year = {1983},
	bdsk-url-1 = {http://www.jstor.org/stable/2045516}}

@article{PhahoferSpohn2002,
	author = {M. Pr{\"a}hofer and H. Spohn},
	date-modified = {2012-02-03 01:49:18 +0000},
	journal = {J. Stat. Phys.},
	note = {arXiv:math.PR/0105240},
	owner = {leo},
	pages = {1071--1106},
	timestamp = {2010.09.13},
	title = {{Scale invariance of the PNG droplet and the Airy process}},
	volume = {108},
	year = {2002}}

@article{Pukanszky_SL2_1964,
	author = {Pukanszky, L.},
	journal = {Mathematische Annalen},
	number = {2},
	owner = {leo},
	pages = {96-143},
	timestamp = {2010.11.11},
	title = {{The Plancherel formula for the universal covering group of SL(2,R)}},
	volume = {156},
	year = {1964}}

@book{Raftery1996,
	author = {Raftery, A.E. and Lewis, S.M. and Gilks, W.R. and Richardson, S. and Spiegelhalter, D.J.},
	journal = {editors WR Gilks, S. Richardson and DJ Spiegelhalter, Chapman \& Hall, Suffolk, UK},
	pages = {163},
	title = {{Markov chain Monte Carlo in practice}},
	year = {1996}}

@article{Rains2005BCN,
	author = {Rains, E.M.},
	date-added = {2011-09-11 12:07:48 +0000},
	date-modified = {2011-09-11 12:08:30 +0000},
	journal = {Transform. Groups},
	note = {arXiv:math/0112035},
	number = {1},
	pages = {63-132},
	title = {{$BC_n$-symmetric polynomials}},
	volume = {10},
	year = {2005}}

@article{Rains2000,
	author = {Rains, E.M.},
	journal = {arXiv preprint},
	note = {arXiv:math/0006097 [math.CO]},
	title = {Correlation functions for symmetrized increasing subsequences},
	year = {2000}}

@article{Rains2000a,
	abstract = {We show that a wide variety of generalized increasing subsequence
	problems admit a one parameter family of extensions for which we
	can exactly compute the mean length of the longest increasing subsequence.
	By the nature of the extension, this gives upper bounds on the mean
	in the unextended model, which turn out to be asymptotically tight
	for all of the models that have so far been analyzed. A heuristic
	analysis based on this fact gives not just the asymptotic mean but
	also the asymptotic scale factor, again agreeing with all known cases.},
	author = {Eric M. Rains},
	comments = {15 pages, LaTeX. Continuous limits consolidated, other minor changes},
	eprint = {math/0004082},
	oai2identifier = {math/0004082},
	owner = {leo},
	timestamp = {2009.03.12},
	title = {A mean identity for longest increasing subsequence problems},
	url = {http://arxiv.org/abs/math/0004082},
	year = {2000},
	bdsk-url-1 = {http://arxiv.org/abs/math/0004082}}

@article{Ramanujan1919,
	author = {S. Ramanujan},
	date-modified = {2023-08-30 14:49:08 -0400},
	journal = {Proc. Camb. Phil. Soc.},
	note = {Collected Papers of Srinivasa Ramanujan, ed. G. H. Hardy, P. V. Seshu Aiyar and B. M. Wilson. Cambridge University Press (1927), pp. 214--215. Reprinted (1962) by Chelsea, New York},
	owner = {leo},
	pages = {214-216},
	timestamp = {2009.07.26},
	title = {Proof of certain identities in combinatorial analysis},
	volume = {19},
	year = {1919}}

@article{RamirezRiderVirag2006RandomAiry,
	author = {Ramirez, J. and Rider, B. and Virag, B.},
	date-added = {2011-08-03 07:16:56 +0000},
	date-modified = {2018-02-28 19:44:45 +0000},
	journal = {Jour. AMS},
	note = {arXiv:math/0607331 [math.PR]},
	number = {4},
	pages = {919-944},
	title = {{Beta ensembles, stochastic Airy spectrum, and a diffusion}},
	volume = {24},
	year = {2011}}

@techreport{Reshetikhin1988,
	address = {Leningrad},
	author = {Reshetikhin, N.},
	date-added = {2011-06-15 12:44:14 +0400},
	date-modified = {2011-06-15 12:49:08 +0400},
	institution = {LOMI},
	number = {E-4-87 \& E-17-87},
	title = {{Quantized universal enveloping algebras, the Yang-Baxter equation and invariants of links (I \& II)}},
	type = {Preprints},
	year = {1987}}

@book{RieszSzNagy1978,
	address = {Moscow},
	author = {Riesz, F. and Sz.-Nagy, B.},
	date-added = {2011-06-16 12:03:31 +0400},
	date-modified = {2011-06-16 12:05:42 +0400},
	note = {Russian translation},
	publisher = {Mir},
	title = {Lectures on functional analysis},
	year = {1978}}

@article{riesz1923probleme,
	author = {Riesz, M.},
	date-added = {2011-09-30 16:31:49 +0000},
	date-modified = {2011-09-30 16:31:49 +0000},
	journal = {Acta Litt. Acad. Sci. Szeged},
	pages = {209--225},
	title = {Sur le probleme des moments et le th{\'e}oreme de Parseval correspondant},
	volume = {1},
	year = {1923}}

@article{Riordan1969,
	author = {J. Riordan and N. J. A. Sloane},
	journal = {J. Austral. Math. Soc.},
	owner = {leo},
	pages = {278-282},
	timestamp = {2009.06.17},
	title = {The enumeration of rooted trees by total height},
	volume = {10},
	year = {1969}}

@article{Roby92RSK,
	author = {Thomas Roby},
	owner = {leo},
	timestamp = {2010.04.15},
	title = {{Robinson-Schensted Correspondences for Differential Posets}},
	year = {1992}}

@phdthesis{Roby91ThesisRSK,
	author = {T. Roby},
	owner = {leo},
	school = {MIT},
	timestamp = {2010.04.15},
	title = {{Applications and Extensions of Fomin's Generalization of Robinson-Schensted Correspondence to Differential Posets}},
	year = {1991}}

@article{Rockner1996,
	author = {Rockner, M.},
	title = {{Dirichlet forms on infinite-dimensional$\backslash$ manifold-like" state spaces: a survey of recent results and some prospects for the future}}}

@article{RomikSniady2011,
	author = {Romik, D. and Sniady, P.},
	date-modified = {2015-03-12 12:31:52 +0000},
	journal = {{Ann. Probab.}},
	note = {arXiv:1111.0575 [math.PR]},
	number = {2},
	owner = {leo},
	pages = {682-737},
	timestamp = {2013.07.23},
	title = {{Jeu de taquin dynamics on infinite Young tableaux and second class particles}},
	volume = {43},
	year = {2015}}

@article{rozhkovskaya1997multiplicative,
	author = {Rozhkovskaya, N.},
	journal = {Jour. Math. Sci. (New York)},
	note = {in Russian: Zap. Nauchn. Sem. POMI {\bf{}240\/} (1997), 245--256},
	number = {5},
	pages = {3600-3608},
	publisher = {St. Petersburg Department of Steklov Institute of Mathematics, Russian Academy of Sciences},
	title = {{Multiplicative distributions on Young graph}},
	volume = {96},
	year = {1999}}

@article{Ruggiero2009,
	author = {Ruggiero, M.},
	title = {{On the representation of Fleming-Viot models from a Bayesian perspective}},
	year = {2009}}

@article{Ruggiero2007,
	author = {Ruggiero, M.},
	title = {{Bayesian countable representation of some population genetics diffusions}},
	year = {2007}}

@article{Ruggiero2007b,
	author = {Ruggiero, M.},
	journal = {Local Organizing Committee},
	title = {{Bayesian Nonparametric Construction of Fleming-Viot Models in Population Genetics}},
	year = {2007}}

@article{Ruggiero2009a,
	author = {Ruggiero, M. and Walker, S.G.},
	date-modified = {2018-02-28 19:49:16 +0000},
	journal = {Electron. Commun. Probab.},
	pages = {501--517},
	title = {{Countable representation for infinite dimensional diffusions derived from the two-parameter Poisson-Dirichlet process}},
	volume = {14},
	year = {2009}}

@article{Ruggiero2007a,
	author = {Ruggiero, M. and Walker, S.G.},
	journal = {Preprint},
	title = {{Construction and stationary distribution of the Fleming-Viot process with viability selection}},
	year = {2007}}

@book{sagan2001symmetric,
	author = {Sagan, B.E.},
	isbn = {0387950672},
	publisher = {Springer Verlag},
	title = {{The symmetric group: representations, combinatorial algorithms, and symmetric functions}},
	year = {2001}}

@article{Sag87,
	author = {Sagan, B.E.},
	journal = {J. Comb. Theo. A},
	owner = {leo},
	pages = {62-103},
	timestamp = {2010.04.12},
	title = {{Shifted tableaux, Schur Q-functions, and a conjecture of Stanley}},
	volume = {45},
	year = {1987}}

@article{sagan1990robinson,
	author = {Sagan, B. and Stanley, R.},
	date-modified = {2011-11-14 17:31:26 +0000},
	journal = {Journal of Combinatorial Theory, Series A},
	number = {2},
	pages = {161--193},
	publisher = {Elsevier},
	title = {{Robinson-Schensted algorithms for skew tableaux}},
	volume = {55},
	year = {1990}}

@article{SasamotoSpohn2010,
	author = {Sasamoto, T. and Spohn, H.},
	date-added = {2013-09-05 22:39:32 +0000},
	date-modified = {2013-09-05 22:40:47 +0000},
	journal = {Nuclear Physics B},
	note = {arXiv:1002.1879 [cond-mat.stat-mech]},
	number = {3},
	pages = {523-542},
	title = {{Exact height distributions for the KPZ equation with narrow wedge initial condition}},
	volume = {834},
	year = {2010}}

@article{SasamotoWadati1998,
	author = {Sasamoto, T. and Wadati, M.},
	date-added = {2013-05-20 17:14:31 +0000},
	date-modified = {2013-05-20 17:15:18 +0000},
	journal = {J. Phys. A},
	pages = {6057--6071},
	title = {{Exact results for one-dimensional totally asymmetric diffusion models}},
	volume = {31},
	year = {1998}}

@article{Schensted1961,
	author = {Schensted, C.},
	date-added = {2013-04-21 00:05:48 +0000},
	date-modified = {2013-05-10 11:45:46 +0000},
	journal = {Canad. J. Math.},
	pages = {179-191},
	title = {Longest increasing and decreasing subsequences},
	volume = {13},
	year = {1961}}

@article{schied1997geometric,
	author = {Schied, A.},
	date-modified = {2018-02-28 19:46:40 +0000},
	journal = {Ann. Probab.},
	number = {3},
	pages = {1160--1179},
	publisher = {Institute of Mathematical Statistics},
	title = {{Geometric aspects of Fleming-Viot and Dawson-Watanabe processes}},
	volume = {25},
	year = {1997}}

@article{schied1996geometric,
	author = {Schied, A.},
	publisher = {Citeseer},
	title = {{Geometric aspects of Fleming-Viot and superprocesses}},
	year = {1996}}

@article{schmuland1995local,
	author = {Schmuland, B.},
	publisher = {de Gruyter, Berlin},
	title = {On the local property for positivity preserving coercive forms, Dirichlet forms and stochastic processes},
	year = {1995}}

@article{schmuland1991result,
	author = {Schmuland, B.},
	journal = {Journal of Applied Probability},
	number = {2},
	pages = {253--267},
	publisher = {Applied Probability Trust},
	title = {{A result on the infinitely many neutral alleles diffusion model}},
	volume = {28},
	year = {1991}}

@article{Schur1911,
	author = {I. Schur},
	journal = {J. Reine Angew. Math.},
	owner = {leo},
	pages = {155-250},
	timestamp = {2009.03.26},
	title = {{\"Uber die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrocheme lineare Substitionen}},
	volume = {139},
	year = {1911}}

@article{TyanShanski1973,
	author = {Semenov-Tian-Shansky, M.},
	date-added = {2013-10-15 23:38:04 +0000},
	date-modified = {2013-10-31 23:01:56 +0000},
	journal = {{Zapiski Nauchnykh Seminarov LOMI}},
	pages = {53-65},
	title = {{A certain property of the Kirillov integral}},
	volume = {37},
	year = {1973}}

@article{Seppalainen2012,
	author = {Sepp{\"a}l{\"a}inen, T.},
	date-modified = {2015-04-01 16:33:52 +0000},
	journal = {{Ann. Probab.}},
	note = {arXiv:0911.2446 [math.PR]},
	pages = {19-73},
	title = {{Scaling for a one-dimensional directed polymer with boundary conditions}},
	volume = {40(1)},
	year = {2012}}

@article{sergeev1999howe,
	author = {Sergeev, AN},
	journal = {Represent. Theory},
	pages = {416--434},
	title = {{The Howe duality and the projective representations of symmetric groups}},
	volume = {3},
	year = {1999}}

@article{Sergeev1984,
	author = {Sergeev, A.N.},
	date-added = {2011-06-19 20:41:48 +0400},
	date-modified = {2011-06-19 20:43:09 +0400},
	journal = {Matematicheskii Sbornik},
	number = {3},
	pages = {422-430},
	title = {{The tensor algebra of the identity representation as a module over the Lie superalgebras Gl(n,m) and Q(n)}},
	volume = {165},
	year = {1984}}

@inproceedings{SV09c,
	author = {Sergeev, A.N. and Veselov, A.P.},
	booktitle = {Proceedings of XVI International Congress on Mathematical Physics (Prague, August 2009)},
	date-added = {2011-09-11 12:10:56 +0000},
	date-modified = {2011-09-11 12:13:22 +0000},
	note = {arXiv:0910.5463},
	pages = {333-337},
	publisher = {World Scientific},
	title = {Quantum Calogero-Moser systems: A view from infinity},
	year = {2010}}

@article{SV09a,
	author = {Sergeev, A.N. and Veselov, A.P.},
	date-added = {2011-09-11 12:09:05 +0000},
	date-modified = {2011-09-11 12:10:22 +0000},
	journal = {Adv. Math.},
	note = {arXiv:0807.3858},
	pages = {1687--1726},
	title = {{$BC_\infty$ Calogero-Moser operator and super Jacobi polynomials}},
	volume = {222},
	year = {2009}}

@article{SV09b,
	author = {Sergeev, A.N. and Veselov, A.P.},
	date-added = {2011-09-11 12:10:27 +0000},
	date-modified = {2011-09-11 12:10:54 +0000},
	note = {arXiv:0910.1984},
	title = {Calogero-Moser operators in infinite dimension},
	year = {2009}}

@article{Sheffield2007GFF,
	author = {Sheffield, S.},
	date-added = {2012-04-03 22:51:19 +0000},
	date-modified = {2018-02-28 19:39:09 +0000},
	journal = {Probab. Theory Relat. Fields},
	note = {arXiv:math/0312099 [math.PR]},
	number = {3-4},
	pages = {521--541},
	title = {Gaussian free fields for mathematicians},
	volume = {139},
	year = {2007},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=2322706}}

@article{Sheffield2008,
	author = {Sheffield, S.},
	date-added = {2012-02-03 00:22:32 +0000},
	date-modified = {2012-02-03 00:52:09 +0000},
	journal = {Ast\'erisque},
	note = {arXiv:math/0304049 [math.PR]},
	title = {Random surfaces},
	volume = {304},
	year = {2005}}

@article{Shepp1966,
	author = {Shepp, LA and Lloyd, SP},
	date-modified = {2018-02-28 19:46:00 +0000},
	journal = {Trans. AMS},
	pages = {340--357},
	publisher = {American Mathematical Society},
	title = {{Ordered cycle lengths in a random permutation}},
	year = {1966}}

@article{Shiga1990,
	author = {Tokuzo Shiga},
	journal = {J . Math. Kyoto Univ.},
	number = {2},
	owner = {leo},
	pages = {245-279},
	timestamp = {2009.08.30},
	title = {A stochastic equation based on a {P}oisson system for a class o f measure-valued diffusion processes},
	volume = {30},
	year = {1990}}

@article{Shiga1981,
	author = {Tokuzo Shiga},
	journal = {J. Math. Kyoto Univ.},
	number = {1},
	owner = {leo},
	pages = {133-151},
	timestamp = {2009.07.19},
	title = {Diffusion processes in population genetics},
	volume = {21},
	year = {1981}}

@book{ShiryaevProb,
	author = {Shiryaev, A.N.},
	date-added = {2012-09-09 16:23:12 +0000},
	date-modified = {2012-09-09 16:24:20 +0000},
	publisher = {Springer},
	title = {Probability},
	year = {1995}}

@book{Simon2005,
	author = {Simon, B.},
	date-modified = {2018-10-24 11:14:10 -0400},
	owner = {leo},
	publisher = {AMS},
	series = {Mathematical Surveys and Monographs},
	timestamp = {2009.11.23},
	title = {Trace Ideals and Their Applications: Second Edition},
	volume = {120},
	year = {2005}}

@article{Sivic2008,
	author = {Sivic, J. and Russell, B.C. and Zisserman, A. and Freeman, W.T. and Efros, A.A.},
	booktitle = {Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR-08)},
	pages = {1--8},
	title = {{Unsupervised discovery of visual object class hierarchies}},
	year = {2008}}

@article{Slavnov2010Integral,
	author = {N. A. Slavnov},
	owner = {leo},
	timestamp = {2010.05.30},
	title = {Integral operators with the generalized sine-kernel on the real axis}}

@article{SmirnovTurbiner1995Hiddensl2,
	author = {Smirnov, Y.F. and Turbiner, A.},
	date-added = {2011-08-03 07:51:26 +0000},
	date-modified = {2011-08-03 07:52:28 +0000},
	note = {arXiv:funct-an/9512002},
	title = {Hidden sl2-algebra of finite-difference equations},
	year = {1995}}

@article{Sniady2013,
	author = {Sniady, P.},
	date-modified = {2015-03-12 12:34:04 +0000},
	journal = {SIAM Journal on Discrete Mathematics},
	note = {arXiv:1307.5645 [math.CO]},
	number = {2},
	owner = {leo},
	pages = {598-630},
	timestamp = {2013.07.23},
	title = {{Robinson--Schensted--Knuth Algorithm, Jeu de Taquin, and Kerov--Vershik Measures on Infinite Tableaux}},
	volume = {28},
	year = {2014}}

@article{Soshnikov2000,
	abstract = {The paper contains an exposition of recent as well as old enough results
	on determinantal random point fields. We start with some general
	theorems including the proofs of the necessary and sufficient condition
	for the existence of the determinantal random point field with Hermitian
	kernel and a criterion for the weak convergence of its distribution.
	In the second section we proceed with the examples of the determinantal
	random point fields from Quantum Mechanics, Statistical Mechanics,
	Random Matrix Theory, Probability Theory, Representation Theory and
	Ergodic Theory. In connection with the Theory of Renewal Processes
	we characterize all determinantal random point fields in R^1 and
	Z^1 with independent identically distributed spacings. In the third
	section we study the translation invariant determinantal random point
	fields and prove the mixing property of any multiplicity and the
	absolute continuity of the spectra. In the fourth (and the last)
	section we discuss the proofs of the Central Limit Theorem for the
	number of particles in the growing box and the Functional Central
	Limit Theorem for the empirical distribution function of spacings.},
	author = {Soshnikov, A.},
	date-modified = {2018-02-06 02:15:04 +0000},
	journal = {Russian Mathematical Surveys},
	note = {arXiv:math/0002099 [math.PR]},
	number = {5},
	pages = {923--975},
	title = {Determinantal random point fields},
	volume = {55},
	year = {2000}}

@article{Speicher2009,
	abstract = {Free probability theory was created by Dan Voiculescu around 1985,
	motivated by his efforts to understand special classes of von Neumann
	algebras. His discovery in 1991 that also random matrices satisfy
	asymptotically the freeness relation transformed the theory dramatically.
	Not only did this yield spectacular results about the structure of
	operator algebras, but it also brought new concepts and tools into
	the realm of random matrix theory. In the following we will give,
	mostly from the random matrix point of view, a survey on some of
	the basic ideas and results of free probability theory.},
	author = {Roland Speicher},
	comments = {21 pages; my contribution for the Handbook on Random Matrix Theory, to be published by Oxford University Press},
	eprint = {0911.0087},
	oai2identifier = {0911.0087},
	owner = {leo},
	timestamp = {2010.11.01},
	title = {Free Probability Theory},
	year = {2009}}

@article{SpiridonovZhedanov2000spectral,
	author = {Spiridonov, V. and Zhedanov, A.},
	date-added = {2012-10-20 20:57:18 +0000},
	date-modified = {2016-08-02 03:00:14 +0000},
	journal = {Commun. Math. Phys.},
	number = {1},
	pages = {49--83},
	publisher = {Springer},
	title = {{Spectral transformation chains and some new biorthogonal rational functions}},
	volume = {210},
	year = {2000}}

@article{Spitzer1970,
	author = {Spitzer, F.},
	date-added = {2013-05-11 00:53:21 +0000},
	date-modified = {2013-05-11 00:54:23 +0000},
	journal = {Adv. Math.},
	number = {2},
	pages = {246-290},
	title = {{Interaction of Markov processes}},
	volume = {5},
	year = {1970}}

@article{Spohn2012,
	author = {Spohn, H.},
	date-added = {2013-10-14 00:30:49 +0000},
	date-modified = {2013-10-14 00:31:26 +0000},
	journal = {Random Matrix Theory, Interacting Particle Systems and Integrable Systems},
	note = {arXiv:1201.0645 [cond-mat.stat-mech]},
	number = {4.3},
	title = {{KPZ Scaling Theory and the Semi-discrete Directed Polymer Model}},
	volume = {65},
	year = {2014}}

@article{stanley2010plancherel,
	author = {Stanley, R.},
	journal = {The Ramanujan Journal},
	pages = {1--15},
	publisher = {Springer},
	title = {{Some combinatorial properties of hook lengths, contents, and parts of partitions}},
	year = {2010}}

@book{Stanley1999,
	address = {Cambridge},
	author = {Stanley, R.},
	date-modified = {2013-04-07 00:25:38 +0000},
	note = {With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin},
	owner = {leo},
	publisher = {Cambridge University Press},
	timestamp = {2009.03.11},
	title = {Enumerative {C}ombinatorics. {V}ol. 2},
	year = {2001}}

@book{Stanley1997,
	address = {Cambridge},
	author = {Stanley, R.},
	date-modified = {2011-11-14 17:31:21 +0000},
	note = {With a foreword by Gian-Carlo Rota, Corrected reprint of the 1986 original.},
	owner = {leo},
	publisher = {Cambridge University Press},
	timestamp = {2009.03.11},
	title = {Enumerative {C}ombinatorics. {V}ol. 1},
	year = {1997}}

@incollection{stanley1990variations,
	address = {New York},
	author = {Stanley, R.},
	booktitle = {Invariant theory and tableaux ({M}inneapolis, {MN}, 1988)},
	date-added = {2011-11-14 17:30:33 +0000},
	date-modified = {2011-11-14 17:30:50 +0000},
	pages = {145--165},
	publisher = {Springer},
	series = {IMA Vol. Math. Appl.},
	title = {Variations on differential posets},
	volume = {19},
	year = {1990},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=1035494}}

@article{stanley1988differential,
	author = {Stanley, R.},
	date-modified = {2018-02-28 19:42:45 +0000},
	journal = {Jour. AMS},
	number = {4},
	owner = {leo},
	pages = {919-961},
	timestamp = {2010.11.07},
	title = {Differential Posets},
	volume = {1},
	year = {1988}}

@article{Stembridge1997,
	author = {John Stembridge},
	date-modified = {2018-02-28 19:44:38 +0000},
	journal = {Trans. AMS},
	owner = {leo},
	pages = {763-788},
	timestamp = {2009.03.16},
	title = {Enriched P-Partitions},
	volume = {349},
	year = {1997}}

@article{Stembridge1994minuscule,
	author = {Stembridge, J.},
	coden = {DUMJAO},
	date-added = {2011-11-08 16:59:07 +0000},
	date-modified = {2014-10-25 19:08:55 +0000},
	doi = {10.1215/S0012-7094-94-07320-1},
	fjournal = {Duke Mathematical Journal},
	issn = {0012-7094},
	journal = {Duke J. Math.},
	number = {2},
	pages = {469--490},
	title = {On minuscule representations, plane partitions and involutions in complex {L}ie groups},
	url = {http://dx.doi.org/10.1215/S0012-7094-94-07320-1},
	volume = {73},
	year = {1994},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=1262215},
	bdsk-url-2 = {http://dx.doi.org/10.1215/S0012-7094-94-07320-1}}

@article{Stembridge1992_QSchur,
	author = {Stembridge, J.R.},
	date-added = {2011-04-22 08:40:53 +0400},
	date-modified = {2011-04-22 08:42:38 +0400},
	journal = {J. Algebraic Combin.},
	number = {1},
	pages = {71-95},
	title = {{On Schur's Q-functions and the primitive idempotents of a commutative Hecke algebra}},
	volume = {1},
	year = {1992}}

@article{Stembridge1992ProjRepHyperoct,
	author = {Stembridge, J.},
	date-added = {2011-08-03 07:22:07 +0000},
	date-modified = {2011-08-03 07:23:00 +0000},
	journal = {Journal of algebra},
	number = {2},
	pages = {396--453},
	title = {The projective representations of the hyperoctahedral group},
	volume = {145},
	year = {1992}}

@article{stembridge1990nonintersecting,
	author = {Stembridge, J.R.},
	journal = {Adv. math},
	number = {1},
	pages = {96--131},
	title = {{Nonintersecting paths, pfaffians and plane partitions}},
	volume = {83},
	year = {1990}}

@article{Stembridge1989,
	author = {Stembridge, J.},
	journal = {Advances in Math.},
	owner = {leo},
	pages = {87-134},
	timestamp = {2009.04.11},
	title = {Shifted tableaux and the projective representations of symmetric groups},
	volume = {74},
	year = {1989}}

@article{Stembridge1985,
	author = {Stembridge, J.},
	date-modified = {2011-11-14 17:32:19 +0000},
	journal = {J. Algebra},
	owner = {leo},
	pages = {439-444},
	timestamp = {2009.03.26},
	title = {A characterization of supersymmetric polynomials},
	volume = {95},
	year = {1985}}

@article{Stoyanov2004,
	author = {Stoyanov, J.},
	date-added = {2013-10-13 20:12:03 +0000},
	date-modified = {2013-10-13 20:12:29 +0000},
	journal = {J. Appl. Prob.},
	pages = {281--294},
	title = {{Stieltjes classes for moment-indeterminate probability distributions}},
	volume = {41},
	year = {2004}}

@article{Strahov2009,
	abstract = {We consider a point process on one-dimensional lattice originated
	from the harmonic analysis on the infinite symmetric group, and defined
	by the z-measures with the deformation (Jack) parameter 2. We derive
	an exact Pfaffian formula for the correlation function of this process.
	Namely, we prove that the correlation function is given as a Pfaffian
	with a matrix kernel. The kernel is given in terms of the Gauss hypergeometric
	functions, and can be considered as a matrix analogue of the Hypergeometric
	kernel introduced by A. Borodin and G. Olshanski. Our result holds
	for all values of admissible complex parameters.},
	author = {Strahov, E.},
	comments = {38 pages},
	eprint = {0905.1994},
	journal = {Adv. Math.},
	note = {arXiv:0905.1994 [math-ph]},
	number = {1},
	oai2identifier = {0905.1994},
	owner = {leo},
	pages = {130--168},
	timestamp = {2010.02.27},
	title = {{The z-measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel}},
	volume = {224},
	year = {2010}}

@article{strahov2009z,
	author = {Strahov, E.},
	journal = {Journal of Algebra},
	note = {arXiv:0904.1719 [math.RT]},
	number = {2},
	pages = {349--370},
	publisher = {Elsevier},
	title = {{Z-measures on partitions related to the infinite Gelfand pair $(S (2\infty), H (\infty))$}},
	volume = {323},
	year = {2010}}

@article{Strahov2007,
	abstract = {In the present paper we construct and solve a differential model for
	the q-analog of the Plancherel growth process. The construction is
	based on a deformation of the Makrov-Krein correspondence between
	continual diagrams and probability distributions.},
	author = {Eugene Strahov},
	comments = {33 pages},
	eprint = {0706.3292},
	oai2identifier = {0706.3292},
	owner = {leo},
	timestamp = {2009.04.13},
	title = {A Differential Model for the Deformation of the Plancherel Growth Process},
	url = {http://arxiv.org/abs/0706.3292},
	year = {2007},
	bdsk-url-1 = {http://arxiv.org/abs/0706.3292}}

@incollection{StratilaVoiculescu1982,
	address = {Warsaw},
	author = {Stratila, S. and Voiculescu, D.},
	booktitle = {Spectral Theory, Banach Center Publications},
	date-added = {2011-06-15 11:00:13 +0400},
	date-modified = {2011-06-15 11:01:49 +0400},
	pages = {415-434},
	publisher = {PWN},
	title = {A survey on representations of the unitary group {$U(\infty)$}},
	volume = {8},
	year = {1982}}

@book{Stroock1996,
	author = {Stroock, D.W.},
	title = {{Dirichlet forms \& symmetric Markov processes, by M. Fukushima, Y. Oshima, and M. Takeda; Dirichlet forms, by Zhi-Ming Ma and Michael Rockner, books survey}},
	year = {1996}}

@article{Takacs1991,
	author = {Lajos Tak{\'a}cs},
	journal = {Advances in Applied Probability},
	number = {3},
	owner = {leo},
	pages = {557-585},
	timestamp = {2009.06.17},
	title = {A Bernoulli Excursion and Its Various Applications},
	volume = {23},
	year = {1991}}

@article{Takacs1986,
	author = {L. Tak{\'a}cs},
	journal = {J. Statist. Planning Inf.},
	owner = {leo},
	pages = {123-142},
	timestamp = {2009.06.17},
	title = {Some asymptotic formulas for lattice paths},
	volume = {14},
	year = {1986}}

@article{Teh2006a,
	author = {Teh, Y.W.},
	booktitle = {Proceedings of the 21st International Conference on Computational Linguistics and the 44th annual meeting of the Association for Computational Linguistics},
	organization = {Association for Computational Linguistics},
	pages = {985-992},
	title = {{A hierarchical Bayesian language model based on Pitman-Yor processes}},
	year = {2006}}

@article{Teh2006,
	author = {Teh, Y.W. and Jordan, M.I. and Beal, M.J. and Blei, D.M.},
	journal = {Journal of the American Statistical Association},
	number = {476},
	pages = {1566--1581},
	publisher = {Citeseer},
	title = {{Hierarchical dirichlet processes}},
	volume = {101},
	year = {2006}}

@conference{Teh2009,
	author = {Yee Whye Teh},
	booktitle = {{Gatsby Computational Neuroscience Unit University College London}},
	owner = {leo},
	timestamp = {2010.01.12},
	title = {{An Introduction to Bayesian Nonparametric Modelling}},
	year = {2009}}

@article{Teh2007,
	author = {Y. W. Teh},
	note = {Submitted to Encyclopedia of Machine Learning},
	title = {{Dirichlet Processes}},
	year = {2007}}

@article{ThibonUng1996QuantumQuasiSymm,
	author = {Thibon, J.-Y. and Ung, B.-C.-V.},
	date-added = {2011-08-03 08:00:07 +0000},
	date-modified = {2011-08-03 08:00:47 +0000},
	journal = {Journal of Physics A: Mathematical and General},
	title = {Quantum quasi-symmetric functions and Hecke algebras},
	year = {1996}}

@incollection{Thoma1984,
	author = {Thoma, E.},
	booktitle = {Operator Algebras and Group Representations},
	date-added = {2011-06-15 10:51:30 +0400},
	date-modified = {2011-06-15 10:53:06 +0400},
	pages = {211-216},
	publisher = {Pitman},
	title = {Characters of infinite groups},
	volume = {2},
	year = {1984}}

@incollection{Thoma1972,
	address = {New York},
	author = {Thoma, E.},
	booktitle = {L. Notes Math},
	owner = {leo},
	pages = {321-323},
	publisher = {Springer},
	timestamp = {2014.01.25},
	title = {{Characters of the group $GL(\infty,q)$}},
	volume = {266},
	year = {1972}}

@article{Thoma1964,
	author = {Thoma, E.},
	date-modified = {2011-06-15 10:52:02 +0400},
	journal = {Math. Zeitschr},
	owner = {leo},
	pages = {40-61},
	timestamp = {2009.03.26},
	title = {Die unzerlegbaren, positive-definiten {K}lassenfunktionen der abz\"ahlbar unendlichen, symmetrischen {G}ruppe},
	volume = {85},
	year = {1964}}

@article{tierz2010schur,
	author = {Tierz, M.},
	journal = {Journal of Mathematical Physics},
	pages = {063509},
	title = {{Schur polynomials and biorthogonal random matrix ensembles}},
	volume = {51},
	year = {2010}}

@article{Tracy1991,
	author = {C. A. Tracy},
	journal = {Commun. Math. Phys.},
	number = {2},
	owner = {leo},
	pages = {297-311},
	timestamp = {2009.12.03},
	title = {{Asymptotics of a $\tau$-function arising in the two--dimensional Ising model}},
	volume = {142},
	year = {1991}}

@article{TW_ASEP3,
	author = {Tracy, C. and Widom, H.},
	date-added = {2013-09-21 17:36:00 +0000},
	date-modified = {2013-09-21 17:36:38 +0000},
	journal = {J. Stat. Phys.},
	note = {arXiv:1205.4054 [math.PR]},
	pages = {1-12},
	title = {{The Bose Gas and Asymmetric Simple Exclusion Process on the Half-Line}},
	volume = {150},
	year = {2013}}

@article{TW_ASEP2,
	author = {Tracy, C. and Widom, H.},
	date-added = {2013-09-21 17:35:03 +0000},
	date-modified = {2013-09-21 17:35:52 +0000},
	journal = {Commun. Math. Phys.},
	note = {arXiv:0807.1713 [math.PR]},
	pages = {129-154},
	title = {{Asymptotics in ASEP with step initial condition}},
	volume = {290},
	year = {2009}}

@article{TW_ASEP4,
	author = {Tracy, C. and Widom, H.},
	date-added = {2013-09-21 17:36:40 +0000},
	date-modified = {2013-09-21 17:37:24 +0000},
	journal = {J. Stat. Phys.},
	note = {arXiv:0907.5192 [math.PR]},
	pages = {825--838},
	title = {{On ASEP with step Bernoulli initial condition}},
	volume = {137},
	year = {2009}}

@article{TW_ASEP1,
	author = {Tracy, C. and Widom, H.},
	date-added = {2013-09-21 17:32:34 +0000},
	date-modified = {2018-02-28 19:49:00 +0000},
	journal = {Comm. Math. Phys},
	note = {arXiv:0704.2633 [math.PR]. Erratum: Commun. Math. Phys., 304:875--878, 2011.},
	pages = {815--844},
	title = {{Integral formulas for the asymmetric simple exclusion process}},
	volume = {279},
	year = {2008}}

@article{TracyWidom2006Pearcey,
	author = {Tracy, C. and Widom, H.},
	date-added = {2012-10-17 16:16:26 +0000},
	date-modified = {2015-10-27 22:43:29 +0000},
	journal = {Commun. Math. Phys.},
	note = {arXiv:math.PR/0412005},
	number = {2},
	pages = {381-400},
	title = {The {P}earcey process},
	volume = {263},
	year = {2006}}

@article{Tracy2004,
	abstract = {To each partition $\lambda$ with distinct parts we assign the probability
	$Q_\lambda(x) P_\lambda(y)/Z$ where $Q_\lambda$ and $P_\lambda$ are
	the Schur $Q$-functions and $Z$ is a normalization constant. This
	measure, which we call the shifted Schur measure, is analogous to
	the much-studied Schur measure. For the specialization of the first
	$m$ coordinates of $x$ and the first $n$ coordinates of $y$ equal
	to $\alpha$ ($0<\alpha<1$) and the rest equal to zero, we derive
	a limit law for $\lambda_1$ as $m,n\ra\infty$ with $\tau=m/n$ fixed.
	For the Schur measure the $\alpha$-specialization limit law was derived
	by Johansson. Our main result implies that the two limit laws are
	identical.},
	author = {Tracy, C.A. and Widom, H.},
	comments = {35 pages, 2 figures. Version 3 adds a section on the Poisson limit of the shifted Schur measure},
	date-modified = {2014-10-25 19:08:48 +0000},
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@article{Vershik1997,
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@article{Macdonald1971padic,
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@article{Macdonald2000orthpoly,
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@article{Vershik1996StatMech,
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@article{Vershik1986a,
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	volume = {34},
	year = {1986}}

@article{Vershik1985,
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	note = {{In the appendix of translation editor to G. James, {Representation theory of symmetric groups (Russian edition)}}, Moscow, Mir.},
	title = {{Symmetric Functions and K--functor}},
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@article{Vershik1975ergodic,
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@article{VK07,
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@article{VK98,
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@article{Kerov1990,
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@article{VK89Hecke,
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	title = {{Characters and realizations of infinite-dimensional Hecke algebra and knot invariants}},
	volume = {38},
	year = {1989}}

@article{vershik1987locally,
	author = {Vershik, A. and Kerov, S.},
	issn = {1072-3374},
	journal = {Journal of Mathematical Sciences},
	number = {2},
	pages = {1701--1733},
	publisher = {Springer},
	title = {{Locally semisimple algebras. Combinatorial theory and the $K_0$-functor}},
	volume = {38},
	year = {1987}}

@article{Vershik1986,
	author = {A. Vershik and S. Kerov},
	date-modified = {2014-10-25 23:15:58 +0000},
	journal = {SIAM J. Alg. Disc. Math.},
	number = {1},
	owner = {leo},
	pages = {116-124},
	timestamp = {2009.05.12},
	title = {The characters of the Infinite Symmetric Group and Probability Properties of the {R}obinson-{S}hensted-{K}nuth algorithm},
	volume = {7},
	year = {1986}}

@article{VershikKerov_LimShape1985,
	author = {Vershik, A.M. and Kerov, S.V.},
	journal = {Funktsional. Anal. i Prilozhen.},
	note = {English translation: Funct. Anal. Appl. \textbf{19} (1985), 21---31},
	number = {1},
	owner = {leo},
	pages = {25-36},
	timestamp = {2010.12.03},
	title = {Asymptotics of the largest and the typical dimensions of irreducible representations of a symmetric group},
	volume = {19},
	year = {1985}}

@incollection{VK1984Kfunctor,
	address = {Boston, MA},
	author = {Vershik, A. and Kerov, S.},
	booktitle = {Operator algebras and group representations, {V}ol. {II} ({N}eptun, 1980)},
	date-added = {2011-11-14 17:49:20 +0000},
	date-modified = {2011-11-14 17:50:33 +0000},
	pages = {23--32},
	publisher = {Pitman},
	series = {Monogr. Stud. Math.},
	title = {Characters, factor representations and {$K$}-functor of the infinite symmetric group},
	volume = {18},
	year = {1984}}

@article{VK82CharactersU,
	author = {Vershik, A. and Kerov, S.},
	date-added = {2011-11-14 17:48:02 +0000},
	date-modified = {2016-08-08 00:48:42 +0000},
	fjournal = {Doklady Akademii Nauk SSSR},
	journal = {Dokl. Akad. Nauk SSSR},
	number = {2},
	pages = {272--276},
	title = {Characters and factor-representations of the infinite unitary group},
	volume = {267},
	year = {1982},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=681202}}

@article{VK1981Characters,
	author = {Vershik, A. and Kerov, S.},
	date-added = {2011-11-14 17:47:12 +0000},
	date-modified = {2011-11-14 17:47:27 +0000},
	fjournal = {Doklady Akademii Nauk SSSR},
	journal = {Dokl. Akad. Nauk SSSR},
	number = {5},
	pages = {1037--1040},
	title = {Characters and factor representations of the infinite symmetric group},
	volume = {257},
	year = {1981},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=614033}}

@article{VK81AsymptoticTheory,
	author = {Vershik, A. and Kerov, S.},
	date-added = {2011-11-14 17:44:42 +0000},
	date-modified = {2012-06-25 18:22:34 +0000},
	fjournal = {Akademiya Nauk SSSR. Funktsional\cprime ny\u\i\ Analiz i ego Prilozheniya},
	journal = {Funktsional. Anal. i Prilozhen.},
	mrreviewer = {G. L. Litvinov},
	number = {4},
	pages = {15--27, 96},
	title = {Asymptotic theory of the characters of the symmetric group},
	volume = {15},
	year = {1981},
	bdsk-url-1 = {http://www.ams.org/mathscinet-getitem?mr=639197}}

@article{VershikKerov_LimShape1077,
	author = {Vershik, A.M. and Kerov, S.V.},
	journal = {Doklady AN SSSR},
	note = {English translation: Soviet Mathematics Doklady \textbf{18} (1977), 527---531},
	number = {6},
	owner = {leo},
	pages = {1024--1027},
	timestamp = {2010.12.03},
	title = {{Asymptotics of the Plancherel measure of the symmetric group and the limiting form of Young tableaux}},
	volume = {233},
	year = {1977}}

@article{VershikNikitin2011,
	author = {Vershik, A. and Nikitin, P.},
	date-added = {2011-07-15 16:05:58 +0400},
	date-modified = {2011-11-14 17:03:31 +0000},
	journal = {Functional Analysis and Its Applications},
	note = {arXiv:1102.4425 [math.RT]},
	number = {1},
	pages = {13-24},
	title = {Description of the characters and factor representations of the infinite symmetric inverse semigroup},
	volume = {45},
	year = {2011}}

@article{VershikNikitin2006,
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	date-modified = {2011-11-14 17:03:41 +0000},
	journal = {Functional Analysis and Its Applications},
	note = {arXiv:math/0610879 [math.RT]},
	number = {3},
	pages = {165-172},
	title = {Traces on infinite-dimensional brauer algebras},
	volume = {40},
	year = {2006}}

@article{Schmidt1978,
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	pages = {72--88},
	title = {{Limit measures arising in the asymptotic theory of the symmetric group}},
	volume = {22},
	year = {1978}}

@article{Vershik1977,
	author = {Vershik, AM and Shimdt, AA},
	journal = {Theory of Probability and its Applications},
	pages = {70},
	title = {{Limit Measures Arising in the Asymptotic Theory of Symmetric Groups. I.}},
	volume = {22},
	year = {1977}}

@article{VS1977,
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@book{Vilenkin-SpecFunc,
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	title = {{Representations of Lie groups and special functions}},
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@article{Vilenkin-Klimyk-DAN_UKR_1988,
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	title = {{Representations of the group $SU(1, 1)$, and the Krawtchouk-Meixner functions}},
	year = {1988}}

@article{Voiculescu1976,
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	year = {1976}}

@article{Voloshin1974,
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@article{vuletic2009generalization,
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	pages = {2789--2804},
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@article{vuletic2007shifted,
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	year = {2007}}

@article{Walker1999,
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	publisher = {Blackwell Publishing; Royal Statistical Society},
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	year = {1999}}

@article{Walker2007a,
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	title = {{A Fleming-Viot process and Bayesian nonparametrics}},
	volume = {17},
	year = {2007}}

@article{Walker2007,
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@article{warren2005dyson,
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	number = {19},
	pages = {573--590},
	title = {{Dyson's Brownian motions, intertwining and interlacing}},
	volume = {12},
	year = {2007}}

@article{Watterson1976reversibility,
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@article{Wenzl1988,
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@book{Weyl1946,
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	title = {{The Classical Groups. Their Invariants and Representations}},
	year = {1997}}

@electronic{Wiki-NNG,
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@book{wilf1989combinatorial,
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	title = {{Combinatorial algorithms: an update}},
	year = {1989}}

@book{Wilf1990,
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	title = {Generatingfunctionology},
	year = {1990}}

@phdthesis{worley1984theory,
	author = {Worley, D.R.},
	school = {MIT, Dept. of Mathematics},
	title = {{A theory of shifted Young tableaux}},
	year = {1984}}

@article{ZeldovichMolchanov,
	author = {Zel'dovich, Ya. and Molchanov, S. and Ruzmaikin, A. and Sokolov, D.},
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	journal = {{Soviet Physics Uspekhi}},
	number = {5},
	pages = {353},
	title = {{Intermittency in random media}},
	volume = {30},
	year = {1987}}

@book{Zelevinsky_Hopf,
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	publisher = {Springer-Verlag},
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	title = {{Representations of Finite Classical Groups: A Hopf algebra approach}},
	year = {1981}}

@book{Zhelobenko-book-eng,
	address = {Providence, RI},
	author = {Zhelobenko, D.},
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	publisher = {Amer. Math. Soc.},
	title = {{Compact Lie groups and their representations}},
	year = {1973}}

@article{ZinnJustin20096Vertex,
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	note = {arXiv:0901.0665 [math-ph]},
	title = {{Six-Vertex, Loop and Tiling models: Integrability and Combinatorics}},
	year = {2009}}

@book{Zipf1932,
	author = {G. Zipf},
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	title = {{Selective Studies and the Principle of Relative Frequency in Language}},
	year = {1932}}

@article{Zirnbauer2010,
	abstract = {Physical systems exhibiting stochastic or chaotic behavior are often
	amenable to treatment by random matrix models. In deciding on a good
	choice of model, random matrix physics is constrained and guided
	by symmetry considerations. The notion of 'symmetry class' (not to
	be confused with 'universality class') expresses the relevance of
	symmetries as an organizational principle. Dyson, in his 1962 paper
	referred to as the Threefold Way, gave the prime classification of
	random matrix ensembles based on a quantum mechanical setting with
	symmetries. In this article we review Dyson's Threefold Way from
	a modern perspective. We then describe a minimal extension of Dyson's
	setting to incorporate the physics of chiral Dirac fermions and disordered
	superconductors. In this minimally extended setting, where Hilbert
	space is replaced by Fock space equipped with the anti-unitary operation
	of particle-hole conjugation, symmetry classes are in one-to-one
	correspondence with the large families of Riemannian symmetric spaces.},
	author = {Martin R. Zirnbauer},
	comments = {article contributed to the Oxford Handbook of Random Matrix Theory, 22 pages},
	date-modified = {2016-01-23 18:07:41 +0000},
	eprint = {1001.0722},
	note = {arXiv:1001.0722 [math-ph]},
	oai2identifier = {1001.0722},
	owner = {leo},
	timestamp = {2010.11.01},
	title = {Symmetry Classes},
	year = {2010}}

@book{Erdelyi1953,
	editor = {A. Erd{\'e}lyi},
	owner = {leo},
	publisher = {McGraw--Hill},
	timestamp = {2009.11.26},
	title = {{Higher transcendental functions}},
	year = {1953}}

@article{ImamuraSasamoto2011current,
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	note = {arXiv:1011.4588 [cond-mat.stat-mech]},
	number = {5},
	pages = {919--930},
	publisher = {Springer},
	title = {{Current moments of 1D ASEP by duality}},
	volume = {142},
	year = {2011}}

@article{Liggett1973infinite_zerorange,
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	journal = {Ann. Probab.},
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	title = {An infinite particle system with zero range interactions},
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	year = {1973}}

@article{Rezakhanlou1991hydrodynamics,
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	journal = {Commun. Math. Phys.},
	number = {3},
	pages = {417--448},
	publisher = {Springer},
	title = {{Hydrodynamic limit for attractive particle systems on $Z^d$}},
	volume = {140},
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