Scaling limit of the corrector in stochastic homogenization

Abstract

In the homogenization of divergence-form equations with random coefficients, a central role is played by the corrector. We focus on a discrete space setting and on dimension $3$ and more. Under a minor smoothness assumption on the law of the random coefficients, we identify the scaling limit of the corrector, which is akin to a Gaussian free field. This completes the argument started in [Ann. Probab. 44 (2016) 3207–3233].