Reluctant walks tend to exit the quarter-plane in which they are constrained, but this work shows how to randomly sample large reluctant walks anyway.
Since the package is registered in Python's central repository, you can install it using pip:
pip install reluctant_walks
Although the package will degrade gracefully, it has some dependencies for certain of its functionalities:
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The Sage environment, to solve the equation necessary to compute the best slope for any family of quarter-plane walk. (Without Sage, it is possible to experiment on the "79 non-trivial small stepset models" for which we have precomputed the best slope with some accuracy.)
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Either GenRGenS or Maple as a backend to randomly sample walks given an algebraic grammar, if you wish to be able to randomly generate walks.
In addition, it is recommended to have matplotlib to visualize the walks, and Jupyter Notebook to experiment with the package. See the notebook folder for examples.
Below is a single walk of size 2000 in green, on a backdrop of many other walks that were also sampled, but which do not remain in the upper-right quarter-plane. There are further such examples in the VisualizingWalks.ipynb notebook.
Bousquet-Mélou, Mireille, and Marni Mishna (2010). "Walks with small steps in the quarter plane." Contemporary Mathematics, 520, pp. 1-40.
Lumbroso, Jeremie, Marni Mishna, and Yann Ponty (2017). "Taming Reluctant Random Walks in the Positive Quadrant." Electronic Notes in Discrete Mathematics (59), pp. 99-114.