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.
Entropy and drift for gibbs measures on geometrically finite manifolds / Gekhtman, I.; Tiozzo, G.. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 373:4(2020), pp. 2949-2980. [10.1090/tran/8036]
Entropy and drift for gibbs measures on geometrically finite manifolds
Tiozzo G.
2020
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.| File | Dimensione | Formato | |
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