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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 mm translations on an arbitrary nilmanifold under mild assumptions on the size of mm. For several classical classes of nilmanifolds, we show m=2m=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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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}
}

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18 pages