We study quantitatively the effective large-scale behavior of discrete elliptic equations on the
lattice\mathbb Z^ d Z d with random coefficients. The theory of stochastic homogenization …

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

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 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 consider the well-trodden ground of the problem of the homogenization of random
integral functionals. When the integrand has standard growth conditions, the qualitative …

We discuss variational formulas for the law of large numbers limits of certain models of
motion in a random medium: namely, the limiting time constant for last-passage percolation …

We study the heat kernel and the Green's function on the infinite supercritical percolation
cluster in dimension d≥ 2 and prove a quantitative homogenization theorem for these …

The main goal of this paper is to define and study new methods for the computation of
effective coefficients in the homogenization of divergence-form operators with random …