42 citations · 66 across the 18 of their papers we have counts for
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math.PR2004
Boundaries and harmonic functions for random walks with random transition probabilities
Vadim A. Kaimanovich, Yuri Kifer, Ben-Zion Rubshtein
The usual random walk on a group (homogeneous both in time and in space) is determined by a probability measure on the group. In a random walk with random transition probabilities…
math.FA2004
Boundary amenability of hyperbolic spaces
Vadim A. Kaimanovich
It is well-known that a Kleinian group is amenable if and only if it is elementary. We establish an analogous property for equivalence relations and foliations with Gromov hyperbol…
math.FA2004
Amenability and the Liouville property
Vadim A. Kaimanovich
We present a new approach to the amenability of groupoids (both in the measure theoretical and the topological setups) based on using Markov operators. We introduce the notion of a…