Quenched Central Limit Theorem for Random Walks in Doubly Stochastic Random Environment

Bálint Tóth

Quenched Central Limit Theorem for Random Walks in Doubly Stochastic Random Environment

Probability 2017-10-03 v3

Authors: Bálint Tóth

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.

Keywords

random walk in random environment central limit theorem random walks

Cite

@article{arxiv.1704.06072,
  title  = {Quenched Central Limit Theorem for Random Walks in Doubly Stochastic Random Environment},
  author = {Bálint Tóth},
  journal= {arXiv preprint arXiv:1704.06072},
  year   = {2017}
}

Comments

18 pages. The proof of quenched tightness, which was deficient in the earlier version, is completed

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