Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization

Abstract

In the present contribution we establish quantitative results on the periodic approximation of the corrector equation for the stochastic homogenization of linear elliptic equations in divergence form, when the diffusion coefficients satisfy a spectral gap estimate in probability, and for $d>2$. The main difference with respect to the first part of [Gloria-Otto, arXiv:1409.0801] is that we avoid here the use of Green's functions and more directly rely on the De Giorgi-Nash-Moser theory.

References in corpus (4)

• An optimal error estimate in stochastic homogenization of discrete elliptic equations
• Quantitative results on the corrector equation in stochastic homogenization
• Correlation structure of the corrector in stochastic homogenization
• Noise-stability and central limit theorems for effective resistance of random electric networks

Cited by in corpus (1)

• Quantitative results on the corrector equation in stochastic homogenization