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

• Andres, Sebastian ^[2] ; Deuschel, Jean-Dominique ^[1] ; Slowik, Martin ^[1]
  1. [1] Technical University of Berlin

     Technical University of Berlin

     Berlin, Stadt, Alemania

     
  2. [2] Rheinische Friedrich-Wilhelms Universität Bonn
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 43, Nº. 4, 2015, págs. 1866-1891
• Idioma: inglés
• DOI: 10.1214/14-AOP921
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• Resumen

  • We study a continuous time random walk, X, on Zd in an environment of random conductances taking values in (0,∞). 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.