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