English

A coupling between random walks in random environments and Brox's diffusion

Probability 2024-10-24 v1

Abstract

It is known that a properly rescaled version of Sinai's random walk converges in distribution to Brox's diffusion. In this article we quantify this convergence by considering a specific coupling between Sinai's walk and Brox's diffusion. Our method relies on convergence results for martingale problems considered in the rough path setting.

Keywords

Cite

@article{arxiv.2410.17776,
  title  = {A coupling between random walks in random environments and Brox's diffusion},
  author = {Xi Geng and Mihai Gradinaru and Samy Tindel},
  journal= {arXiv preprint arXiv:2410.17776},
  year   = {2024}
}
R2 v1 2026-06-28T19:32:45.204Z