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.
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}
}