Moment bounds for the corrector in stochastic homogenization of a percolation model
نویسندگان
چکیده
We study the corrector equation in stochastic homogenization for a simplified Bernoulli percolation model on Z, 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.
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