Regularity of the entropy for random walks on hyperbolic groups

Abstract

We consider nondegenerate, finitely supported random walks on a finitely generated Gromov hyperbolic group. We show that the entropy and the escape rate are Lipschitz functions of the probability if the support remains constant.

Published in at http://dx.doi.org/10.1214/12-AOP748 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• The ratio set of the harmonic measure of a random walk on a hyperbolic group
• Randomly growing braid on three strands and the manta ray
• Noncommutative Ergodic Theorems
• Rate of Escape of Random Walks on Regular Languages and Free Products by Amalgamation of Finite Groups

Cited by in corpus (3)

• Deviation inequalities and CLT for random walks on acylindrically hyperbolic groups
• Renewal theory for random walks on surface groups
• Differentiating the entropy of random walks on hyperbolic groups