Quantitative stochastic homogenization of uniformly convex energy functionals

I will describe a new quantitative approach to stochastic homogenization for elliptic equations in divergence form. This gives the first quantitative results for nonlinear equations, but also new results for linear equations. The idea is to show that the energy of a minimizer spreads evenly over large scales, which can be thought of as a kind of quantitative compensated compactness.