The corrector in stochastic homogenization: Near-optimal rates with optimal stochastic integrability

Antoine Gloria, Felix Otto

Published 2015-10-28Version 1

We consider uniformly elliptic coefficient fields that are randomly distributed according to a stationary ensemble of a finite range of dependence. We show that the gradient $\nabla\phi$ of the corrector $\phi$, when spatially averaged over a scale $R\gg 1$ decays like $R^{-\alpha}$ for any $\alpha<\frac{d}{2}$. We establish these rates on the level of Gaussian bounds in terms of the stochastic integrability.