Moment bounds for the corrector in stochastic homogenization of a percolation model

Abstract

We study the corrector equation in stochastic homogenization for a simplified Bernoulli percolation model on Z^d, d > 2. The model is obtained from the classical {0,1}-Bernoulli bond percolation by conditioning all bonds parallel to the first coordinate direction to be open. As a main result we prove (in fact for a slightly more general model) that stationary correctors exist and that all finite moments of the corrector are bounded. This extends a previous result in [8], where uniformly elliptic conductances are treated, to the degenerate case. Our argument is based on estimates on the gradient of the elliptic Green's function.