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May 2008 Asymptotic entropy and Green speed for random walks on countable groups
Sébastien Blachère, Peter Haïssinsky, Pierre Mathieu
Ann. Probab. 36(3): 1134-1152 (May 2008). DOI: 10.1214/07-AOP356

Abstract

We study asymptotic properties of the Green metric associated with transient random walks on countable groups. We prove that the rate of escape of the random walk computed in the Green metric equals its asymptotic entropy. The proof relies on integral representations of both quantities with the extended Martin kernel. In the case of finitely generated groups, where this result is known (Benjamini and Peres [Probab. Theory Related Fields 98 (1994) 91–112]), we give an alternative proof relying on a version of the so-called fundamental inequality (relating the rate of escape, the entropy and the logarithmic volume growth) extended to random walks with unbounded support.

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Sébastien Blachère. Peter Haïssinsky. Pierre Mathieu. "Asymptotic entropy and Green speed for random walks on countable groups." Ann. Probab. 36 (3) 1134 - 1152, May 2008. https://doi.org/10.1214/07-AOP356

Information

Published: May 2008
First available in Project Euclid: 9 April 2008

zbMATH: 1146.60008
MathSciNet: MR2408585
Digital Object Identifier: 10.1214/07-AOP356

Subjects:
Primary: 34B27, 60B15

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 3 • May 2008
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