## The Annals of Probability

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

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

https://projecteuclid.org/euclid.aop/1433341322

Digital Object Identifier
doi:10.1214/14-AOP921

Mathematical Reviews number (MathSciNet)
MR3353817

Zentralblatt MATH identifier
1325.60037

#### 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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