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November 2018 Quenched central limit theorem for random walks in doubly stochastic random environment
Bálint Tóth
Ann. Probab. 46(6): 3558-3577 (November 2018). DOI: 10.1214/18-AOP1256

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.

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Bálint Tóth. "Quenched central limit theorem for random walks in doubly stochastic random environment." Ann. Probab. 46 (6) 3558 - 3577, November 2018. https://doi.org/10.1214/18-AOP1256

Information

Received: 1 October 2017; Revised: 1 December 2017; Published: November 2018
First available in Project Euclid: 25 September 2018

zbMATH: 06975493
MathSciNet: MR3857862
Digital Object Identifier: 10.1214/18-AOP1256

Subjects:
Primary: 60F05, 60G99, 60K37

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 6 • November 2018
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