57 citations · 93 across the 8 of their papers we have counts for
10 papers
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…
Integral criteria of hyperbolicity for graphs and groups
Victor Gerasimov, Leonid Potyagailo
We establish three criteria of hyperbolicity of a graph in terms of ``average width of geodesic bigons''. In particular we prove that if the ratio of the Van Kampen area of a geode…
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…
Similar relatively hyperbolic actions of a group
Victor Gerasimov, Leonid Potyagailo
Let a discrete group possess two convergence actions by homeomorphisms on compacta and . Consider the following question: does there exist a convergence action $G{\curve…
Quasiconvexity in the Relatively Hyperbolic Groups
Victor Gerasimov, Leonid Potyagailo
We study different notions of quasiconvexity for a subgroup of a relatively hyperbolic group The first result establishes equivalent conditions for to be relatively qu…
Non-finitely generated relatively hyperbolic groups and Floyd quasiconvexity
Victor Gerasimov, Leonid Potyagailo
The paper consists of two parts. In the first one we show that a relatively hyperbolic group splits as a star graph of groups whose central vertex group is finitely generated a…
Floyd maps to the boundaries of relatively hyperbolic groups
Victor Gerasimov
A continuous equivariant map from the Floyd boundary of a relatively hyperbolic group (RHG for short) to its Bowditch boundary is constructed. Such a map is unique unless the group…
Quasi-isometric maps and Floyd boundaries of relatively hyperbolic groups
V. Gerasimov, L. Potyagailo
We describe the kernel of the canonical map from the Floyd boundary of a relatively hyperbolic group to its Bowditch boundary. Using our methods we then prove that a finitely gener…
Potts model on infinite graphs and the limit of chromatic polynomials
Aldo Procacci, Benedetto Scoppola, Victor Gerasimov
Given an infinite graph $\GI$ quasi-transitive and amenable with maximum degree $\D$, we show that reduced ground state degeneracy per site $W_r(\GI,q)$ of the q-state antiferromag…