Equidistribution of affine random walks on some nilmanifolds

Weikun He; Tsviqa Lakrec; Elon Lindenstrauss

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

Equidistribution of affine random walks on some nilmanifolds

Weikun He, Tsviqa Lakrec, Elon Lindenstrauss^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Scopus citations

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.

Original language	English
Title of host publication	Analysis at Large
Subtitle of host publication	Dedicated to the Life and Work of Jean Bourgain
Publisher	Springer International Publishing
Pages	131-171
Number of pages	41
ISBN (Electronic)	9783031053313
ISBN (Print)	9783031053306
DOIs	https://doi.org/10.1007/978-3-031-05331-3_7
State	Published - 1 Nov 2022

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022.

Access to Document

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

Cite this

@inbook{3a010a92fdf64587ae14d0f10fcd5e3a,

title = "Equidistribution of affine random walks on some nilmanifolds",

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.",

author = "Weikun He and Tsviqa Lakrec and Elon Lindenstrauss",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2022.",

year = "2022",

month = nov,

day = "1",

doi = "10.1007/978-3-031-05331-3_7",

language = "אנגלית",

isbn = "9783031053306",

pages = "131--171",

booktitle = "Analysis at Large",

publisher = "Springer International Publishing",

}

TY - CHAP

T1 - Equidistribution of affine random walks on some nilmanifolds

AU - He, Weikun

AU - Lakrec, Tsviqa

AU - Lindenstrauss, Elon

PY - 2022/11/1

Y1 - 2022/11/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85153995159&partnerID=8YFLogxK

U2 - 10.1007/978-3-031-05331-3_7

DO - 10.1007/978-3-031-05331-3_7

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.chapter???

AN - SCOPUS:85153995159

SN - 9783031053306

SP - 131

EP - 171

BT - Analysis at Large

PB - Springer International Publishing

ER -

Equidistribution of affine random walks on some nilmanifolds

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this