  Consider a discrete uniformly elliptic divergence form equation on the $d$
dimensional lattice $\Z^d$ with random coefficients. It has previously been
shown that if the random environment is translational invariant, then the
averaged Green's function together with its first and second differences, are
bounded by the corresponding quantities for the constant coefficient discrete
elliptic equation. It has also been shown that if the random environment is
ergodic, then solutions of the random equation converge under diffusive scaling
to solutions of a homogenized elliptic PDE on $\R^d$. In this paper point-wise
estimates are obtained on the difference between the averaged Green's function
and the homogenized Green's function for certain random environments which are
strongly mixing.
