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Article Dans Une Revue Discrete Analysis Année : 2017

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

Résumé

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.
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Dates et versions

hal-01202000 , version 1 (22-09-2015)
hal-01202000 , version 2 (04-05-2017)

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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⟩
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