Reversibility of a simple random walk on periodic trees
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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 $T$.References
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Additional Information
- Serdar Altok
- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
- Email: saltok@umail.iu.edu
- Received by editor(s): October 3, 2008
- Received by editor(s) in revised form: November 26, 2008
- Published electronically: October 23, 2009
- Communicated by: Richard C. Bradley
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1101-1111
- MSC (2000): Primary 60J10; Secondary 60G50
- DOI: https://doi.org/10.1090/S0002-9939-09-09844-X
- MathSciNet review: 2566575