  It is known that a random walk on $\Z^d$ among i.i.d. uniformly elliptic
random bond conductances verifies a central limit theorem. It is also known
that approximations of the covariance matrix can be obtained by considering
periodic environments. Here we estimate the speed of convergence of this
homogenization result. We obtain similar estimates for finite volume
approximations of the effective conductance and of the lowest Dirichlet
eigenvalue. A lower bound is also given for the variance of the Green function
of a random walk in a random non-negative potential.
