Non-Expanding Random walks on Homogeneous spaces and Diophantine approximation

Abstract

We study non-expanding random walks on the space of affine lattices and establish a new classification theorem for stationary measures. Further, we prove a theorem that relates the genericity with respect to these random walks to Birkhoff genericity. Finally, we apply these theorems to obtain several results in inhomogeneous Diophantine approximation, especially on fractals.

33 Pages, Comments Welcome. arXiv admin note: text overlap with arXiv:1610.05912 by other authors