Homogenization of random convolution energies

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