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 …

One of the principal difficulties in stochastic homogenization is transferring quantitative
ergodic information from the coefficients to the solutions, since the latter are nonlocal …

We investigate volume-element sampling strategies for the stochastic homogenization of
particle-reinforced composites and show, via computational experiments, that an improper …

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 …

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 consider uniformly elliptic coefficient fields that are randomly distributed according to a
stationary ensemble of a finite range of dependence. We show that the gradient and flux …

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 …

The effective large-scale properties of materials with random heterogeneities on a small
scale are typically determined by the method of representative volumes: a sample of the …