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math.DS2020
Central limit theorems for counting measures in coarse negative curvature
Ilya Gekhtman, Samuel J. Taylor, Giulio Tiozzo
We establish central limit theorems for an action of a group G on a hyperbolic space X with respect to the counting measure on a Cayley graph of G. Our techniques allow us to remov…
math.DS2019
Entropy and drift for Gibbs measures on geometrically finite manifolds
Ilya Gekhtman, Giulio Tiozzo
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) me…
math.DS2017★ 3 cited
Equidistribution of closed geodesics along random walk trajectories with respect to the harmonic invariant measure
Ilya Gekhtman
We prove that for suitable random walks on isometry groups of spaces, typical sample paths eventually land on loxodromic elements which equidistribute with respect to a f…