  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 $\Gamma$-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, that can be extended to this `asymptotically-local'
case. As a particular application we derive a homogenization theorem on random
perforated domains.
