Scaling limit of local time of Sinai’s random walk

Abstract

We prove that the local times of a sequence of Sinai’s random walks converge to those of Brox’s diffusion by proper scaling. Our proof is based on the intrinsic branching structure of the random walk and the convergence of the branching processes in random environment.

Keywords

Sinai’s random walk / random environment / local time / Brox’s diffusion / branching process

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