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

Balint Toth

doi:10.1214/18-AOP1256

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

Balint Toth

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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, $L^{2+\varepsilon}$ (rather than $L^2$) integrability condition on the stream tensor. On the way we extend Nash's moment bound to the non-reversible, divergence-free drift case.

Original language	English
Pages (from-to)	3558-3577
Number of pages	20
Journal	Annals of Probability
Volume	46
Issue number	6
Early online date	25 Sept 2018
DOIs	https://doi.org/10.1214/18-AOP1256
Publication status	E-pub ahead of print - 25 Sept 2018

Keywords

random walk in random environment
quenched central limit theorem
Nash bounds

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10.1214/18-AOP1256

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Institute of Mathematical Statistics at https://projecteuclid.org/euclid.aop/1537862440#abstract . Please refer to any applicable terms of use of the publisher.
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Professor Balint A Toth
- Balint.Tothbristol.acuk
- School of Mathematics - Chair in Probability
- Probability, Analysis and Dynamics
- Probability
Person: Academic , Member, Group lead

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N2 - 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, $L^{2+\varepsilon}$ (rather than $L^2$) integrability condition on the stream tensor. On the way we extend Nash's moment bound to the non-reversible, divergence-free drift case.

AB - 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, $L^{2+\varepsilon}$ (rather than $L^2$) integrability condition on the stream tensor. On the way we extend Nash's moment bound to the non-reversible, divergence-free drift case.

KW - random walk in random environment

KW - quenched central limit theorem

KW - Nash bounds

U2 - 10.1214/18-AOP1256

DO - 10.1214/18-AOP1256

M3 - Article (Academic Journal)

SN - 0091-1798

VL - 46

SP - 3558

EP - 3577

JO - Annals of Probability

JF - Annals of Probability

IS - 6

ER -

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

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Professor Balint A Toth

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