Homogenization of a diffusion in a high-contrast random environment and related Markov semigroups

TL;DR

This paper investigates the long-term behavior of a Markov process driven by a symmetric diffusion in a high-contrast random environment, aiming to identify the limiting semigroup and process under diffusive scaling.

Contribution

It provides a rigorous characterization of the asymptotic behavior and limit objects for diffusions in complex random environments, extending existing homogenization theory.

Findings

Identification of the limit semigroup and process

Description of the homogenization effect in high-contrast environments

Mathematical framework for analyzing diffusions in random media

Abstract

The goal of the paper is to describe the large time behaviour of a Markov process associated with a symmetric diffusion in a high-contrast random environment and to characterize the limit semigroup and the limit process under the diffusive scaling.