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Semisimple random walks on the torus

Part of: Ergodic theory Exponential sums and character sums Linear algebraic groups and related topics Sequences and sets

Published online by Cambridge University Press:  03 March 2025

WEIKUN HE  and
NICOLAS DE SAXCÉ
WEIKUN HE
Affiliation:
Institute of Mathematics, Academy of Mathematics and System Science, CAS, Zhongguancun East Road 55, Beijing 100190, P. R. China (e-mail: heweikun@amss.ac.cn)
NICOLAS DE SAXCÉ*
Affiliation:
CNRS – Université Sorbonne Paris Nord, LAGA, 93430 Villetaneuse, France
*
e-mail: desaxce@math.univ-paris13.fr
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Abstract

We study linear random walks on the torus and show a quantitative equidistribution statement, under the assumption that the Zariski closure of the acting group is semisimple.

Keywords

equidistributionsum-productLyapunov exponentFourier decay

MSC classification

Primary: 37A17: Homogeneous flows 11B75: Other combinatorial number theory
Secondary: 37A45: Relations with number theory and harmonic analysis 11L07: Estimates on exponential sums 20G30: Linear algebraic groups over global fields and their integers

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 45 , Issue 10 , October 2025 , pp. 3090 - 3147
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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