10 citations · 13 across the 6 of their papers we have counts for
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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…
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…
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…