Differentiating the entropy of random walks on hyperbolic groups

P. Mathieu (1)

1 I2M - Institut de Mathématiques de Marseille

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.

Domaines: Mathématiques [math]

P. Mathieu. Differentiating the entropy of random walks on hyperbolic groups. Annals of Probability, 2015, 43 (1), pp.166-187. ⟨10.1214/13-AOP901⟩. ⟨hal-01266478⟩