Scaling limit of the corrector in stochastic homogenization

TL;DR

This paper determines the scaling limit of the corrector in stochastic homogenization for divergence-form equations with random coefficients in discrete space, showing it converges to a Gaussian free field in dimensions three and higher.

Contribution

It completes the analysis of the corrector's scaling limit in stochastic homogenization, establishing its convergence to a Gaussian free field in higher dimensions.

Findings

Corrector's scaling limit identified as a Gaussian free field

Results apply to discrete space and dimensions three and above

Advances understanding of stochastic homogenization in higher dimensions

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. Completing the argument started in previous work, we identify the scaling limit of the corrector, which is akin to a Gaussian free field.