Arbeitsgemeinschaft: Quantitative Stochastic Homogenization

Abstract

Homogenization means approximating the effective, i.e. macroscopic, behavior of a heterogeneous medium by a homogeneous one, which amounts to a substantial conceptual and practical reduction of complexity. Stochastic homogenization means that one is considering an ensemble of, i.e. a probability measure on, such heterogeneities (typically expressing a lack of knowledge of the details); and that the effective behavior is also deterministic next to being homogeneous. The aim of this Arbeitsgemeinschaft is to present the recent progress in this field.