Spectral homogenization of reversible random walks on Zd in a random environment

The first result is a homogenization theorem for the Dirichlet eigenvalues of reversible random walks on Zd with stationary and uniformly elliptic conductances. It is then used to prove that the CLT holds in μ-almost all environments and to study the law of the exit times. Applications to the almost sure convergence of capacities and currents are given in the last section.