Entropy and drift for gibbs measures on geometrically finite manifolds

Ilya Gekhtman, Giulio Tiozzo

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)2949-2980
Number of pages32
JournalTransactions of the American Mathematical Society
Volume373
Issue number4
DOIs
StatePublished - 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • General Mathematics

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