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.
|Title of host publication
|Analysis at Large
|Subtitle of host publication
|Dedicated to the Life and Work of Jean Bourgain
|Springer International Publishing
|Number of pages
|Published - 1 Nov 2022
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© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022.