  This paper is concerned with the study of solutions to discrete parabolic
equations in divergence form with random coefficients, and their convergence to
solutions of a homogenized equation.
  In [11] 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 in which
correlations can have arbitrarily small power law decay. Similar results for
discrete elliptic equations were obtained in [12].
