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Central Limit Theorem for Random Walks in Doubly Stochastic Random Environment: H-1 Suffices

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Original languageEnglish
Pages (from-to)4307-4347
Number of pages41
JournalAnnals of Probability
Volume45
Issue number6B
DOIs
DateAccepted/In press - 15 Nov 2016
DatePublished (current) - 12 Dec 2017

Abstract

We prove a central limit theorem under diffusive scaling for the displacement of a random walk on Ζd in stationary and ergodic doubly stochastic random environment, under the Η-1-condition imposed on the drift field. The condition is equivalent to assuming that the stream tensor of the drift field be stationary and square integrable. This improves the best existing result [10], where it is assumed that the stream tensor is in Lmax{2+δ;d}, with δ > 0. Our proof relies on an extension of the relaxed sector condition of [8], and is technically rather simpler than existing earlier proofs of similar results by Oelschläger [19] and Komorowski, Landim and Olla [10].

    Research areas

  • random walk in random environment, central limit theorem, Kipnis-Varadhan theory, sector condition

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