Stochastic homogenization of degenerate integral functionals with linear growth

We study the limit behaviour of sequences of non-convex, vectorial, random integral functionals, defined on W1,1, whose integrands are ergodic and satisfy degenerate linear growth conditions. The latter involve suitable random, scale-dependent weight-functions. Under minimal assumptions on the integrand and on the weight-functions, we show that the sequence of functionals homogenizes to a non-degenerate deterministic functional defined on BV.