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

Published 23 Oct 2024 in math.PR | (2410.17776v1)

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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Authors (3)

  1. Xi Geng 
  2. Mihai Gradinaru 
  3. Samy Tindel 

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