Examples of stable-like random walks on groups of polynomial growth
Probability
2025-09-03 v1
Abstract
We consider several families of long jump random walks on groups of polynomial volume growth which are naturally expected to have a stable-like behavior. We then prove optimal pseudo-Poincar\'e inequalities for these walks. These pseudo-Poincar\'e inequalities allow us to show that the random walks in questions indeed have a stable-like behavior and to obtain detailed estimates.
Keywords
Cite
@article{arxiv.2509.00970,
title = {Examples of stable-like random walks on groups of polynomial growth},
author = {Laurent Saloff-Coste and Ruoqi Zhang},
journal= {arXiv preprint arXiv:2509.00970},
year = {2025}
}