English

Non-Expanding Random walks on Homogeneous spaces and Diophantine approximation

Dynamical Systems 2025-05-06 v4 Number Theory Probability

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.

Keywords

Cite

@article{arxiv.2406.15824,
  title  = {Non-Expanding Random walks on Homogeneous spaces and Diophantine approximation},
  author = {Gaurav Aggarwal and Anish Ghosh},
  journal= {arXiv preprint arXiv:2406.15824},
  year   = {2025}
}

Comments

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