Let G be a countable group which acts by isometries on a separable, but not necessarily
proper, Gromov hyperbolic space X. We say the action of G is weakly hyperbolic if G …

We study random walks on groups, with the feature that, roughly speaking, successive
positions of the walk tend to be “aligned.” We formalize and quantify this property by means …

We study asymptotic properties of the Green metric associated with transient random walks
on countable groups. We prove that the rate of escape of the random walk computed in the …

We present a survey of results related to Milnor's problem on group growth. We discuss the
cases of polynomial growth and exponential but not uniformly exponential growth; the main …

In this paper we study asymptotic properties of symmetric and nondegenerate random walks
on transient hyperbolic groups. We prove a central limit theorem and a law of iterated …

In 1921, George Pólya published a short article [110] posing the following problem. Imagine
a traveller on an infinite regular grid of roads—an infinite Manhattan, without Broadway …

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) …

Asymptotic behaviors of random walks on countable groups Page 1 Asymptotic behaviors of
random walks on countable groups Tianyi Zheng (郑天一) Abstract In this note we survey some …

This article presents the beginning of a metric functional analysis. A major notion is metric
functionals which extends that of horofunctions in metric geometry. Applications of the main …

Abstract We study the Poisson–Furstenberg boundary of random walks on permutational
wreath products. We give a sufficient condition for a group to admit a symmetric measure of …