Strong Convergence to the homogenized limit of elliptic equations with random coefficients II

Consider a discrete uniformly elliptic divergence form equation on the $d$ dimensional lattice ${\mathbb{Z}}^d$ with random coefficients. In [3] rate of convergence results in homogenization and estimates on the difference between the averaged Green’s function and the homogenized Green’s function for random environments which satisfy a Poincar'{e} inequality were obtained. Here these results are extended to certain environments with long range correlations. These environments are simply related via a convolution to environments which do satisfy a Poincar'{e} inequality.