LATTICES OF MATRICES

We study a new class of matrix model, formulated on a lattice, On each site are N states with random energies governed by a gaussian random matrix hamiltonian. The states on different: sites are coupled randoml y. We calculate the density of and correlation between the eigenvalues of the total hamiltonian in the large-N limit, We find that this corr elation exhibits the same type of universal behavior we discovered rec ently. Several derivations of this result are given. This class of ran dom matrices allows us to model the transition between the ''localized '' and ''extended'' regimes within the limited context of random matri x theory.