Quantitative equidistribution of linear random walk on the torus

Abstract

Consider the action of GL_d(Z) on the d-dimensional torus R^d/Z^d. Given a probability measure on GL_d(Z) and a point on the torus, a random walk is defined. In this talk, I will report some recent progress about the equidistribution of such random walks. More precisely, I will talk about quantitative results under the assumption that the acting group has semisimple Zariski closure. This is a generalisation of a theorem of Bourgain, Furman, Lindenstrauss and Mozes. This talk is based on a joint work with Nicolas de Saxcé.

Speaker

Weikun He is an associate professor of Institute of Mathematics, C.A.S. His research Interests are in Arithmetic combinatorics, Homogeneous dynamics, Fractal geometry, Geometry of groups.

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http://www.math.ac.cn/kyry/202202/t20220228_682686.html