Local limit theorems on relatively hyperbolic groups with respect to virtually nilpotent subgroups
Group Theory
2025-07-22 v1 Probability
Abstract
Given a probability measure on a finitely generated group, the local limit problem consists in finding asymptotics of , the probability that the random walk at time is at the origin. We give the classification of all possible local limit theorems, up to bounded error, for finitely supported, symmetric, admissible probability measures on a relatively hyperbolic group with respect to virtually nilpotent subgroups.
Cite
@article{arxiv.2507.15408,
title = {Local limit theorems on relatively hyperbolic groups with respect to virtually nilpotent subgroups},
author = {Matthieu Dussaule},
journal= {arXiv preprint arXiv:2507.15408},
year = {2025}
}