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arXiv · 1904.01187

Entropy and drift for Gibbs measures on geometrically finite manifolds

Ilya Gekhtman·Giulio Tiozzo
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Abstract

We prove a generalization of the fundamental inequality of Guivarc'h relating entropy, drift and critical exponent to Gibbs measures on geometrically finite quotients of CAT(-1) metric spaces. For random walks with finite superexponential moment, we show that the equality is achieved if and only if the Gibbs density is equivalent to the hitting measure. As a corollary, if the action is not convex cocompact, any hitting measure is singular to any Gibbs density.

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Ilya Gekhtman, Giulio Tiozzo. 2019-04-02. Entropy and drift for Gibbs measures on geometrically finite manifolds. https://arxiv.org/abs/1904.01187

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