On Rapid mixing for random walks on nilmanifolds
Dmitry Dolgopyat, Spencer Durham, Minsung Kim
公開日: 2025/10/1
Abstract
We prove rapid mixing for almost all random walks generated by $m$ translations on an arbitrary nilmanifold under mild assumptions on the size of $m$. For several classical classes of nilmanifolds, we show $m=2$ 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.