We give a proof of the sublinear tracking property for sample paths of random walks on
various groups acting on spaces with hyperbolic-like properties. As an application, we prove …

We answer positively a question of Kaimanovich and Vershik from 1979, showing that the
final configuration of lamps for simple random walk on the lamplighter group over Zd (d≥ 3) …

We give a complete description of the Poisson boundary of wreath products $ A\wr
B=\bigoplus_ {B} A\rtimes B $ of countable groups $ A $ and $ B $, for probability measures …

We give a survey of recent results on the Poisson-Furstenberg boundaries of random walks
on groups, and their applications. We describe sufficient conditions for random walk to have …

A resistance network is a connected graph (G, c). The conductance function c_ xy weights
the edges, which are then interpreted as conductors of possibly varying strengths. The …

Answering a question of Benjamini and Schramm (Ann Probab 24 (3): 1219–1238, 1996),
we show that the Poisson boundary of any planar, uniquely absorbing (eg one-ended and …

Abstract We study the Poisson–Furstenberg boundary of random walks on C= A≀ B, where
A= ℤd and B is a finitely generated group having at least 2 elements. We show that for d≥ 5 …

We study random walks on the lampshuffler group FSym (H)⋊ H, where H is a finitely
generated group and FSym (H) is the group of finitary permutations of H. We show that for …

Let (G, µ) be a discrete group with a generating probability measure. Nevo showed that if G
has Kazhdan's property (T), then there exists ɛ> 0 such that the Furstenberg entropy of any …

We prove that random walks on Thompson's group F driven by strictly non-degenerate
finitely supported probability measures μ have a nontrivial Poisson boundary. The proof …