CORRECTOR ESTIMATES FOR ELLIPTIC SYSTEMS WITH RANDOM PERIODIC COEFFICIENTS

We consider the corrector equation for the second order elliptic system on the d-dimensional torus of size L (d >= 2), associated with random coefficients A that are assumed to be coercive and stationary. Using two different approaches we obtain moment bounds on the gradient of the corrector, independent of the domain size L. In the first approach we use Green's function representation. For that we require A to be locally Holder continuous and the distribution of A to satisfy a logarithmic Sobolev inequality. The second method works for nonsmooth (possibly discontinuous) coefficients, and it requires that the statistic of A satisfies a spectral gap estimate.