This talk is concerned with solutions of linear elliptic equations in
divergence form with rapidly oscillating coefficients. One expects that as the
degree of oscillation increases the solution converges to the solution of a
constant coefficient equation. This result was proved in 1980 by Papanicolau
and Varadhan when the coefficients are assumed to be random variables. Here we
are concerned with the rate of convergence. We establish rates of convergence
when the coefficients are iid random variables. The rate depends on the uniform
ellipticity constants for the equation. These results complement previous work
of Naddaf and Spencer. In the Naddaf-Spencer work the coefficients are assumed
to be functions of a Euclidean field theory.