On the concentration of Sinai's walk

Pierre Andreoletti

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On the concentration of Sinai's walk

Pierre Andreoletti

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Abstract

We consider Sinai's random walk in random environment. We prove that for an interval of time [1,n] Sinai's walk sojourns in a small neighborhood of the point of localization for the quasi totality of this amount of time. Moreover the local time at the point of localization normalized by $n$ converges in probability to a well defined random variable of the environment.

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Pierre Andreoletti. 2005-01-26. On the concentration of Sinai's walk. https://arxiv.org/abs/math/0501466

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