Long-time asymptotics of diffusion in random media and related problems

Abstract

For n-dimensional diffusion in Gaussian random fields, with continuous and singular covariances, the leading long-time behaviour of the averaged population is derived by estimating Brownian motion expectations. It is shown how these results are related to the leading low-energy behaviour of the density of states for a particle in a corresponding random potential and to the strong-coupling limit of the free energy of the Pekar-Frolich polaron.