LOCALIZATION FOR RANDOM SCHRODINGER-OPERATORS WITH CORRELATED POTENTIALS

We prove localization at high disorder or low energy for lattice Schrodinger operators with random potentials whose values at different lattice sites are correlated over large distances. The class of admissible random potentials for our multiscale analysis includes potentials with a stationary Gaussian distribution whose covariance function C(x,y) decays as \x-y\-theta, where theta > 0 can be arbitrarily small, and potentials whose probability distribution is a completely analytical Gibbs measure. The result for Gaussian potentials depends on a multivariable form of Nelson's best possible hypercontractive estimate.