The Annals of Probability

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

Bálint Tóth

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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

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

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

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Zentralblatt MATH identifier

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

Random walk in random environment quenched central limit theorem Nash bounds


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.

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