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

2024/10/23 by Xi Geng, Geng, Xi, Mihai Gradinaru +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2410.17776

openalex publication_date 2024/10/23 · openalex created_date 2024/10/27 · openalex updated_date 2026/07/28

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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• Quenched and annealed heat kernel estimates for Brox's diffusion

Related

• From the Sinai's walk to the Brox diffusion using bilinear forms
• Scaling limit of the local time of the Sinai's random walk
• Quenched and annealed heat kernel estimates for Brox's diffusion
• Coupling for features of random walks
• Stein's method for rough paths