Myasnikov (City College of New York) et al. apply the complexity of non-commutative groups
to public key cryptography, assess the generic-case performance of various algorithms, and …

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 …

Semi-invertible multiplicative ergodic theorems establish the existence of an Oseledets
splitting for cocycles of non-invertible linear operators (such as transfer operators) over an …

A result for subadditive ergodic cocycles is proved that provides more delicate information
than Kingman's subadditive ergodic theorem. As an application we deduce a multiplicative …

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 study random walks on metric spaces with contracting isometries. In this first article of the
series, we establish sharp deviation inequalities by adapting Gou\" ezel's pivotal time …

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 …

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 …

We consider a nondegenerate random walk on a locally compact group with finite first
moment. Then, if there are no nonconstant bounded harmonic functions, all the linear drift …

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 …