The focus of this book is the large-scale statistical behavior of solutions of divergence-form
elliptic equations with random coefficients, which is closely related to the long-time …

Since the seminal results by Avellaneda & Lin it is known that elliptic operators with periodic
coefficients enjoy the same regularity theory as the Laplacian on large scales. In a recent …

Since the seminal results by Avellaneda\& Lin it is known that elliptic operators with periodic
coefficients enjoy the same regularity theory as the Laplacian on large scales. In a recent …

This paper is about the homogenization of linear elliptic operators in divergence form with
stationary random coefficients that have only slowly decaying correlations. It deduces …

We give a self-contained introduction of the theory of elliptic homogenization for random
coefficient fields, starting from classical qualitative homogenization. Our exposition of the …

Four quantities are fundamental in homogenization of elliptic systems in divergence form
and in its applications: the field and the flux of the solution operator (applied to a general …

We establish quantitative homogenization, large‐scale regularity, and Liouville results for
the random conductance model on a supercritical (Bernoulli bond) percolation cluster. The …

We consider linear elliptic equations in divergence form with stationary random coefficients
of integrable correlations. We characterize the fluctuations of a macroscopic observable of a …

We study the representative volume element (RVE) method, which is a method to
approximately infer the effective behavior a hom of a stationary random medium. The latter is …

We develop a quantitative theory of stochastic homogenization for linear, uniformly parabolic
equations with coefficients depending on space and time. Inspired by recent works in the …