Quantitative stochastic homogenization of convex integral functionals

We present quantitative results for the homogenization of uniformly convex integral functionals with random coefficients under independence assumptions. The main result is an error estimate for the Dirichlet problem which is algebraic (but sub-optimal) in the size of the error, but optimal in stochastic integrability. As an application, we obtain quenched $C^{0,1}$ estimates for local minimizers of such energy functionals.