Equidistribution of Affine Random Walks on Some Nilmanifolds

Weikun He (), Tsviqa Lakrec () and Elon Lindenstrauss ()
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Weikun He: Korea Institute for Advanced Study
Tsviqa Lakrec: The Hebrew University of Jerusalem, Einstein Institute of Mathematics
Elon Lindenstrauss: The Hebrew University of Jerusalem, Einstein Institute of Mathematics

A chapter in Analysis at Large, 2022, pp 131-171 from Springer

Abstract: Abstract We study quantitative equidistribution in law of affine random walks on nilmanifolds, motivated by a result of Bourgain, Furman, Mozes, and the third named author on the torus. Under certain assumptions, we show that a failure to having fast equidistribution is due to a failure on a factor nilmanifold. Combined with equidistribution results on the torus, this leads to an equidistribution statement on some nilmanifolds such as Heisenberg nilmanifolds. In an appendix we strengthen results of de Saxce and the first named author regarding random walks on the torus by eliminating an assumption on Zariski connectedness of the acting group.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-05331-3_7

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DOI: 10.1007/978-3-031-05331-3_7

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