Homogenization of diffusion in high contrast random media and related Markov semigroups

Abstract

The goal of the paper is to describe the large time behavior of a Markov process associated with a symmetric diffusion in a high contrast random stationary environment and to characterize the limit process under the diffusive scaling.The advantage of the proposed approach is that we explicitly present the limit operator on the extended space. That gives us a possibility to use this operator for approximations of diffusion processes inporous media with random structure of inclusions. We also describe the spectrum of the limit operator.Our approach uses auxiliary Markov processes defined on extended state spaces, as well as tools from homogenization theory in random media.