10 citations · 10 across the 3 of their papers we have counts for
3 papers · 1 filter
Characterization of hyperbolic groups via random walks
Victor Gerasimov, Leonid Potyagailo
Our first result gives a partial converse to a well-known theorem of A. Ancona for hyperbolic groups. We prove that a group , equipped with a symmetric probability measure whose…
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…