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arXiv · 2510.00398

On Rapid mixing for random walks on nilmanifolds

Dmitry Dolgopyat·Spencer Durham·Minsung Kim
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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.

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Dmitry Dolgopyat, Spencer Durham, Minsung Kim. 2025-10-01. On Rapid mixing for random walks on nilmanifolds. https://arxiv.org/abs/2510.00398

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