Analyticity of the entropy and the escape rate of random walks in hyperbolic groups

Sébastien Gouëzel (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

We consider random walks on a non-elementary hyperbolic group endowed with a word distance. To a probability measure on the group are associated two numerical quantities, the rate of escape and the entropy. On the set of admissible probability measures whose support is contained in a given finite set, we show that both quantities depend in an analytic way on the probability measure. Our spectral techniques also give a new proof of the central limit theorem, and imply that the corresponding variance is analytic.

Domaines: Probabilités [math.PR]; Théorie des groupes [math.GR]; Systèmes dynamiques [math.DS]

Sébastien Gouëzel. Analyticity of the entropy and the escape rate of random walks in hyperbolic groups. Discrete Analysis, 2017, 2017 (7), ⟨10.19086/da.1639⟩. ⟨hal-01202000v2⟩