On Rapid mixing for random walks on nilmanifolds
Dynamical Systems
2026-01-16 v3 Differential Geometry
Probability
Abstract
We prove rapid mixing for almost all random walks generated by translations on an arbitrary nilmanifold under mild assumptions on the size of . For several classical classes of nilmanifolds, we show suffices. This provides a partial answer to the question raised in \cite{D02} about the prevalence of rapid mixing for random walks on homogeneous spaces.
Cite
@article{arxiv.2510.00398,
title = {On Rapid mixing for random walks on nilmanifolds},
author = {Dmitry Dolgopyat and Spencer Durham and Minsung Kim},
journal= {arXiv preprint arXiv:2510.00398},
year = {2026}
}
Comments
18 pages