QUENCHED CENTRAL LIMIT THEOREM FOR RANDOM WALKS IN DOUBLY STOCHASTIC RANDOM ENVIRONMENT

摘要

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, L2+epsilon (rather than L-2) integrability condition on the stream tensor. On the way we extend Nash's moment bound to the nonreversible, divergence-free drift case, with unbounded (L2+epsilon) stream tensor. This paper is a sequel of [Ann. Probab. 45 (2017) 4307-4347] and relies on technical results quoted from there.