The Annals of Probability

Invariance principle for the random conductance model in a degenerate ergodic environment

Sebastian Andres, Jean-Dominique Deuschel, and Martin Slowik

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Abstract

We study a continuous time random walk, $X$, on $\mathbb{Z}^{d}$ in an environment of random conductances taking values in $(0,\infty)$. We assume that the law of the conductances is ergodic with respect to space shifts. We prove a quenched invariance principle for $X$ under some moment conditions of the environment. The key result on the sublinearity of the corrector is obtained by Moser’s iteration scheme.

Article information

Source
Ann. Probab., Volume 43, Number 4 (2015), 1866-1891.

Dates
Received: June 2013
Revised: December 2013
First available in Project Euclid: 3 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.aop/1433341322

Digital Object Identifier
doi:10.1214/14-AOP921

Mathematical Reviews number (MathSciNet)
MR3353817

Zentralblatt MATH identifier
1325.60037

Subjects
Primary: 60K37: Processes in random environments 60F17: Functional limit theorems; invariance principles 82C41: Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50]

Keywords
Random conductance model invariance principle corrector Moser iteration ergodic

Citation

Andres, Sebastian; Deuschel, Jean-Dominique; Slowik, Martin. Invariance principle for the random conductance model in a degenerate ergodic environment. Ann. Probab. 43 (2015), no. 4, 1866--1891. doi:10.1214/14-AOP921. https://projecteuclid.org/euclid.aop/1433341322


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