The fundamental inequality of Guivarc'h relates the entropy and the drift of random walks on
groups. It is strict if and only if the random walk does not behave like the uniform measure on …

Completing a strategy of Gouëzel and Lalley, we prove a local limit theorem for the random
walk generated by any symmetric finitely supported probability measure on a non …

We propose the metric notion of strong hyperbolicity as a way of obtaining hyperbolicity with
sharp additional properties. Speci cally, strongly hyperbolic spaces are Gromov hyperbolic …

R.–Considérons une marche aléatoire symétrique à support fini sur un groupe fuchsien
cocompact. Nous montrons que la fonction de Green à son rayon de convergence R décroît …

We show that for every non-elementary hyperbolic group, an associated topological flow
space admits a coding based on a transitive subshift of finite type. Applications include …

We prove pointwise and maximal ergodic theorems for probability-measure-preserving
(PMP) actions of any countable group, provided it admits an essentially free, weakly mixing …

Given a probability measure on a finitely generated group, its Martin boundary is a natural
way to compactify the group using the Green function of the corresponding random walk. For …

Let Γ Γ be a relatively hyperbolic group and let μ μ be an admissible symmetric finitely
supported probability measure on Γ Γ. We extend Floyd–Ancona type inequalities from …

Regularity of the entropy for random walks on hyperbolic groups Page 1 The Annals of
Probability 2013, Vol. 41, No. 5, 3582–3605 DOI: 10.1214/12-AOP748 © Institute of Mathematical …

We present a general new method for constructing pointwise ergodic sequences on
countable groups which is applicable to amenable as well as to non-amenable groups and …