Translator Disclaimer
July 2015 Invariance principle for the random conductance model in a degenerate ergodic environment
Sebastian Andres, Jean-Dominique Deuschel, Martin Slowik
Ann. Probab. 43(4): 1866-1891 (July 2015). DOI: 10.1214/14-AOP921

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.

Citation

Download Citation

Sebastian Andres. Jean-Dominique Deuschel. Martin Slowik. "Invariance principle for the random conductance model in a degenerate ergodic environment." Ann. Probab. 43 (4) 1866 - 1891, July 2015. https://doi.org/10.1214/14-AOP921

Information

Received: 1 June 2013; Revised: 1 December 2013; Published: July 2015
First available in Project Euclid: 3 June 2015

zbMATH: 1325.60037
MathSciNet: MR3353817
Digital Object Identifier: 10.1214/14-AOP921

Subjects:
Primary: 60F17, 60K37, 82C41

Rights: Copyright © 2015 Institute of Mathematical Statistics

JOURNAL ARTICLE
26 PAGES


SHARE
Vol.43 • No. 4 • July 2015
Back to Top