The Annals of Probability

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

Bálint Tóth

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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, $\mathcal{L}^{2+\varepsilon}$ (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
Received: October 2017
Revised: December 2017
First available in Project Euclid: 25 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.aop/1537862440

Digital Object Identifier
doi:10.1214/18-AOP1256

Mathematical Reviews number (MathSciNet)
MR3857862

Zentralblatt MATH identifier
06975493

Subjects
Primary: 60F05: Central limit and other weak theorems 60G99: None of the above, but in this section 60K37: Processes in random environments

Keywords
Random walk in random environment quenched central limit theorem Nash bounds

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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