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arXiv · 1509.06859

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

Sébastien Gouëzel
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Abstract

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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Sébastien Gouëzel. 2017-05-05. Analyticity of the entropy and the escape rate of random walks in hyperbolic groups. https://doi.org/10.19086/da.1639

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