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This paper is concerned with the study of solutions to discrete parabolicequations in divergence form with random coefficients, and their convergence tosolutions of a homogenized equation.  In [11] rate of convergence results in homogenization and estimates on thedifference between the averaged Green's function and the homogenized Green'sfunction for random environments which satisfy a Poincar\'{e} inequality wereobtained. Here these results are extended to certain environments in whichcorrelations can have arbitrarily small power law decay. Similar results fordiscrete elliptic equations were obtained in [12].

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