Quantitative homogenization of degenerate random environments

Abstract

We study discrete linear divergence-form operators with random coecients, also known as the random conductance model. We assume that the conductances are bounded, independent and stationary; the law of a conductance may depend on the orientation of the associated edge. We give a simple necessary and sucient condition for the relaxation of the environment seen by the particle to be diusive, in the sense of every polynomial moment. As a consequence, we derive polynomial moment estimates on the corrector. MSC 2010: 35B27, 35K65, 60K37.