14 citations · 47 across the 23 of their papers we have counts for
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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…
Counting problems in graph products and relatively hyperbolic groups
Ilya Gekhtman, Samuel J. Taylor, Giulio Tiozzo
We study properties of generic elements of groups of isometries of hyperbolic spaces. Under general combinatorial conditions, we prove that loxodromic elements are generic (i.e. th…
The Martin boundary of relatively hyperbolic groups with virtually abelian parabolic subgroups
Matthieu Dussaule, Ilya Gekhtman, Victor Gerasimov +1
Given a probability measure on a finitely generated group, its Martin boundary is a way to compactify the group using the Green's function of the corresponding random walk. We give…
Martin boundary covers Floyd boundary
Ilya Gekhtman, Victor Gerasimov, Leonid Potyagailo +1
For finitely supported random walks on finitely generated groups we prove that the identity map on extends to a continuous equivariant surjection from the Martin boundary t…