Differentiating the entropy of random walks on hyperbolic groups

P. Mathieu

doi:10.1214/13-AOP901

Differentiating the entropy of random walks on hyperbolic groups

Probability 2015-01-12 v3

Authors: P. Mathieu

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Abstract

We show that the asymptotic entropy of a random walk on a nonelementary hyperbolic group, with symmetric and bounded increments, is differentiable and we identify its derivative as a correlation. We also prove similar results for the rate of escape.

Keywords

random walk in random environment random walks random walk on graphs

Cite

@article{arxiv.1209.2020,
  title  = {Differentiating the entropy of random walks on hyperbolic groups},
  author = {P. Mathieu},
  journal= {arXiv preprint arXiv:1209.2020},
  year   = {2015}
}

Comments

Published in at http://dx.doi.org/10.1214/13-AOP901 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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