Quenched central limit theorem for random walks in doubly stochastic random environment

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Abstract

We prove the quenched version of the central limit theorem for the displacement of a random walk in doubly stochastic random environment, under the $H_{-1}$-condition, with slightly stronger, $L^{2+\varepsilon}$ (rather than $L^2$) integrability condition on the stream tensor. On the way we extend Nash's moment bound to the non-reversible, divergence-free drift case.
Original languageEnglish
Pages (from-to)3558-3577
Number of pages20
JournalAnnals of Probability
Volume46
Issue number6
Early online date25 Sep 2018
DOIs
Publication statusE-pub ahead of print - 25 Sep 2018

Keywords

  • random walk in random environment
  • quenched central limit theorem
  • Nash bounds

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