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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Reversibility of a simple random walk on periodic trees


Author: Serdar Altok
Journal: Proc. Amer. Math. Soc. 138 (2010), 1101-1111
MSC (2000): Primary 60J10; Secondary 60G50
Published electronically: October 23, 2009
MathSciNet review: 2566575
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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$.


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Additional Information

Serdar Altok
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: saltok@umail.iu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09844-X
PII: S 0002-9939(09)09844-X
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
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.