  We propose an abstract framework for the homogenization of random functionals
which may contain non-convex terms, based on a two-scale $\Gamma$-convergence
approach and a definition of Young measures on micropatterns which encodes the
profiles of the oscillating functions and of functionals. Our abstract result
is a lower bound for such energies in terms of a cell problem (on large
expanding cells) and the $\Gamma$-limits of the functionals at the microscale.
We show that our method allows to retrieve the results of Dal Maso and Modica
in the well-known case of the stochastic homogenization of convex Lagrangians.
As an application, we also show how our method allows to stochastically
homogenize a variational problem introduced and studied by Alberti and
M\"uller, which is a paradigm of a problem where an additional mesoscale arises
naturally due to the non-convexity of the singular perturbation (lower order)
terms in the functional.
