activity
20172022
most citedMartin boundary covers Floyd boundary

10 citations · 13 across the 5 of their papers we have counts for

collaborators

10 papers

math.DS2022

Equidistribution of hyperbolic groups in homogeneous spaces

Ilya Gekhtman, Samuel J. Taylor, Giulio Tiozzo

We prove that infinite orbits of Zariski dense hyperbolic groups equidistribute in homogeneous spaces, in the sense that the family of measures obtained by averaging along spheres…

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.GR2018

Entropy and drift for word metric on relatively hyperbolic groups

Matthieu Dussaule, Ilya Gekhtman

We are interested in the Guivarc'h inequality for admissible random walks on finitely generated relatively hyperbolic groups, endowed with a word metric. We show that for random wa…

math.GT2018

A central limit theorem for random closed geodesics: proof of the Chas-Li-Maskit conjecture

Ilya Gekhtman, Samuel J. Taylor, Giulio Tiozzo

We prove a central limit theorem for the length of closed geodesics in any compact orientable hyperbolic surface. In the special case of a hyperbolic pair of pants, this settles a…

math.GR2018

Critical exponents of invariant random subgroups in negative curvature

Ilya Gekhtman, Arie Levit

Let be a proper geodesic Gromov hyperbolic metric space and let be a cocompact group of isometries of admitting a uniform lattice. Let be the Hausdorff dimension of…