Examples of stable-like random walks on groups of polynomial growth
Laurent Saloff-Coste, Ruoqi Zhang
Published: 2025/8/31
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.