Semisimple random walks on the torus

TL;DR

This paper investigates how linear random walks on the torus distribute over time, providing quantitative results under the condition that the acting group's Zariski closure is semisimple.

Contribution

It offers a new quantitative equidistribution result for linear random walks on the torus with semisimple Zariski closure assumptions.

Findings

Established a quantitative equidistribution theorem.

Demonstrated the importance of semisimplicity in the acting group's Zariski closure.

Extended understanding of random walk behavior on compact abelian groups.

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.