The phenomenon of macroscopic homogenization is illustrated with a simple e
xample of diffusion. We examine the conditions under which a d-dimensional
simple random walk in a symmetric random media converges to a Brownian moti
on. For d = 1, both the macroscopic homogeneity condition and the diffusion
coefficient can be read from an explicit expression for the Green's functi
on. Except for this case, the two available formulas for the effective diff
usion matrix kappa do not explicit show how macroscopic homogenization take
s place. Using an electrostatic analogy due to Anshelevich, Khanin and Sina
i [AKS], we discuss upper and lower bounds on the diffusion coefficient kap
pa for d > 1.