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

Xi Geng; Mihai Gradinaru; Samy Tindel

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arXiv · 2410.17776

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

Xi Geng·Mihai Gradinaru·Samy Tindel

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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.

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Xi Geng, Mihai Gradinaru, Samy Tindel. 2024-10-23. A coupling between random walks in random environments and Brox's diffusion. https://arxiv.org/abs/2410.17776

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