Equidistribution of affine random walks on some nilmanifolds

Weikun He, Tsviqa Lakrec, Elon Lindenstrauss

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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.

Original languageAmerican English
Title of host publicationAnalysis at Large
Subtitle of host publicationDedicated to the Life and Work of Jean Bourgain
Number of pages41
ISBN (Electronic)9783031053313
StatePublished - 1 Nov 2022

All Science Journal Classification (ASJC) codes

  • General Mathematics


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