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 starting point, we can define a random walk. The topic of this talk is the quantitative equidistribution in law of such random walks. Such results date back to the work of Bourgain-Furman-Lindenstrauss-Mozes. I will present some recent development based on collaborations with Nicolas de Saxce, Tsviqa Lakrec and Elon Lindenstrauss.