Homogenization of random convolution energies

Abstract

We prove a homogenization theorem for a class of quadratic convolution energies with random coefficients. Under suitably stated hypotheses of ergodicity and stationarity, we prove that the Γ-limit of such energy is almost surely a deterministic quadratic Dirichlet-type integral functional, whose integrand can be characterized through an asymptotic formula. The proof of this characterization relies on results on the asymptotic behaviour of subadditive processes. The proof of the limit theorem uses a blow-up technique common for local energies, which can be extended to this ‘asymptotically local’ case. As a particular application, we derive a homogenization theorem on random perforated domains.

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