Journal of Applied Probability

A quenched central limit theorem for reversible random walks in a random environment on Z

Hoang-Chuong Lam

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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.

Article information

Source
J. Appl. Probab., Volume 51, Number 4 (2014), 1051-1064.

Dates
First available in Project Euclid: 20 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.jap/1421763327

Mathematical Reviews number (MathSciNet)
MR3301288

Zentralblatt MATH identifier
06408803

Subjects
Primary: 60J15 60F05: Central limit and other weak theorems
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 60J60: Diffusion processes [See also 58J65]

Keywords
Quenched central limit theorem reversible random walk in random environment

Citation

Lam, Hoang-Chuong. A quenched central limit theorem for reversible random walks in a random environment on Z. J. Appl. Probab. 51 (2014), no. 4, 1051--1064. https://projecteuclid.org/euclid.jap/1421763327


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