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Scaling limit of the local time of the Sinai's random walk (1403.2045v1)

Published 9 Mar 2014 in math.PR

Abstract: We prove that the local times of a sequence of Sinai's random walks convergence to those of Brox's diffusion by proper scaling, which is accord with the result of Seignourel (2000). Our proof is based on the convergence of the branching processes in random environment by Kurtz (1979).