Equidistribution of linear random walks on the torus.

 In this talk, we consider random walks arising from the action of SL_d(Z) on the d-dimensional torus. Quantitative equidistribution in law was first obtained by Bourgain, Furman, Lindenstrauss and Mozes. In this talk I will present a recent progress where the proximality assumption in their result is relaxed. This is based on a joint work with Nicolas de Saxcé.