This is the first of a series of two papers dealing with local limit theorems in relatively
hyperbolic groups. In this first paper, we prove rough estimates for the Green function. Along …

This is the second of a series of two papers dealing with local limit theorems in relatively
hyperbolic groups. In this second paper, we restrict our attention to non-spectrally …

Let $ G $ be a countable group whose action on a metric space $ X $ involves a contracting
isometry. This setting naturally encompasses groups acting on Gromov hyperbolic spaces …

Let $\Gamma $ be a non-elementary relatively hyperbolic group with a finite generating set.
Consider a finitely supported admissible and symmetric probability measure $\mu $ on …

Given a probability measure $\mu $ on a finitely generated group $\Gamma $, the Green
function $ G (x, y| r) $ encodes many properties of the random walk associated with $\mu …

We study random walks on relatively hyperbolic groups whose law is convergent, in the
sense that the derivative of its Green function is finite at the spectral radius. When parabolic …

We study boundaries arising from limits of ratios of transition probabilities for random walks
on relatively hyperbolic groups. We extend, as well as determine significant limitations of, a …

We construct random walks on free products of the form Z 3∗ Z d, with d= 5 or 6 which are
divergent and not spectrally positive recurrent. We then derive a local limit theorem for these …