Proves rapid mixing in random walks on nilmanifolds, highlighting implications for homogeneous spaces.
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 {D02} about the prevalence of rapid mixing for random walks on homogeneous spaces.
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Dolgopyat et al. (2025) studied this question.
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