## The Annals of Probability

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

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

#### Article information

Source
Ann. Probab., Volume 46, Number 6 (2018), 3558-3577.

Dates
Revised: December 2017
First available in Project Euclid: 25 September 2018

https://projecteuclid.org/euclid.aop/1537862440

Digital Object Identifier
doi:10.1214/18-AOP1256

Mathematical Reviews number (MathSciNet)
MR3857862

Zentralblatt MATH identifier
06975493

#### Citation

Tóth, Bálint. Quenched central limit theorem for random walks in doubly stochastic random environment. Ann. Probab. 46 (2018), no. 6, 3558--3577. doi:10.1214/18-AOP1256. https://projecteuclid.org/euclid.aop/1537862440

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