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December 2014 A quenched central limit theorem for reversible random walks in a random environment on Z
Hoang-Chuong Lam
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J. Appl. Probab. 51(4): 1051-1064 (December 2014).

Abstract

The main aim of this paper is to prove the quenched central limit theorem for reversible random walks in a stationary random environment on Z without having the integrability condition on the conductance and without using any martingale. The method shown here is particularly simple and was introduced by Depauw and Derrien [3]. More precisely, for a given realization ω of the environment, we consider the Poisson equation (Pω - I)g = f, and then use the pointwise ergodic theorem in [8] to treat the limit of solutions and then the central limit theorem will be established by the convergence of moments. In particular, there is an analogue to a Markov process with discrete space and the diffusion in a stationary random environment.

Citation

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Hoang-Chuong Lam. "A quenched central limit theorem for reversible random walks in a random environment on Z." J. Appl. Probab. 51 (4) 1051 - 1064, December 2014.

Information

Published: December 2014
First available in Project Euclid: 20 January 2015

zbMATH: 06408803
MathSciNet: MR3301288

Subjects:
Primary: 60F05, 60J15
Secondary: 60J27, 60J60

Rights: Copyright © 2014 Applied Probability Trust

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Vol.51 • No. 4 • December 2014
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