2017-43.md

course	course_year	question_number	tags	title	year
Markov Chains	IB	43	IB 2017 Markov Chains	Paper 3, Section I, H	2017

(a) What does it mean to say that a Markov chain is reversible?

(b) Let $G$ be a finite connected graph on $n$ vertices. What does it mean to say that $X$ is a simple random walk on $G$ ?

Find the unique invariant distribution $\pi$ of $X$.

Show that $X$ is reversible when $X_{0} \sim \pi$.

[You may use, without proof, results about detailed balance equations, but you should state them clearly.]