Reversibility of a simple random walk on periodic trees

Altok, Serdar

doi:10.1090/S0002-9939-09-09844-X

Reversibility of a simple random walk on periodic trees
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Proc. Amer. Math. Soc. 138 (2010), 1101-1111 Request permission

Abstract:

We show that if $\mu$ is a reversible measure for simple random walk on rooted trees whose branches are covers of finite connected directed graphs, then $\mu$ is supported on rooted covers of finite connected undirected graphs. For a given finite connected directed graph $G$ and a cover $T$ of $G$, we give an algorithm to determine whether there exists a finite connected undirected graph whose cover has a branch isomorphic to $T$.

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