Entropy and drift for Gibbs measures on geometrically finite manifolds
Dynamical Systems
2019-05-24 v2 Geometric Topology
Probability
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.
Keywords
Cite
@article{arxiv.1904.01187,
title = {Entropy and drift for Gibbs measures on geometrically finite manifolds},
author = {Ilya Gekhtman and Giulio Tiozzo},
journal= {arXiv preprint arXiv:1904.01187},
year = {2019}
}
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29 pages