Strong convergence to the homogenized limit of elliptic equations with random coefficients II
Joseph G. Conlon, Arash Fahim · Bulletin of the London Mathematical Society · 2013
Consider a discrete uniformly elliptic divergence form equation on the d⩾3 dimensional lattice Zd with random coefficients. In Conlon and Spencer [Trans. Amer. Math. Soc., http://www.math.lsa.umich.edu/~conlon/paper/hom10.pdf], 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 Poincaré inequality were obtained. Here, these results are extended to certain environments in which correlations can have arbitrarily small power law decay. These environments are simply related via a convolution to environments which do satisfy a Poincaré inequality.