42 citations · 66 across the 18 of their papers we have counts for
6 papers · 1 filter
Arboreal structures on groups and the associated boundaries
Anna Erschler, Vadim Kaimanovich
For any countable group with infinite conjugacy classes we construct a family of forests on the group. For each of them there is a random walk on the group with the property that i…
Thompson's group is not Liouville
Vadim A. Kaimanovich
We prove that random walks on Thompson's group driven by strictly non-degenerate finitely supported probability measures have a non-trivial Poisson boundary. The proof cons…
Self-similarity and random walks
Vadim A. Kaimanovich
This is an introductory level survey of some topics from a new branch of fractal analysis -- the theory of self-similar groups. We discuss recent works on random walks on self-simi…
Ergodic properties of boundary actions and Nielsen--Schreier theory
Rostislav Grigorchuk, Vadim A. Kaimanovich, Tatiana Nagnibeda
We study the basic ergodic properties (ergodicity and conservativity) of the action of an arbitrary subgroup of a free group on the boundary with respect to th…
On amenability of automata groups
Laurent Bartholdi, Vadim A. Kaimanovich, Volodymyr V. Nekrashevych
We show that the group of bounded automatic automorphisms of a rooted tree is amenable, which implies amenability of numerous classes of groups generated by finite automata. The pr…
The Subadditive Ergodic Theorem and generic stretching factors for free group automorphisms
Vadim Kaimanovich, Ilya Kapovich, Paul Schupp
Given a free group of rank with a fixed set of free generators we associate to any homomorphism from to a group with a left-invariant semi-norm a gener…