Finite volume approximation of the Anderson model

In the Anderson model on Zd, we consider a sequence of its finite volume approximation { Hk }k and construct a set of sequences composed of the eigenvalues and eigenfunctions of { Hk } in the localized region I which converge to those of H simultaneously. For its proof, Minami's estimate turns out to be important. This result implies that, in the localized region, each eigenfunction behaves almost independently around their centers of localization.