Correlation structure of the corrector in stochastic homogenization
Analysis of PDEs
2016-09-29 v3 Probability
Abstract
Recently, the quantification of errors in the stochastic homogenization of divergence-form operators has witnessed important progress. Our aim now is to go beyond error bounds, and give precise descriptions of the effect of the randomness, in the large-scale limit. This paper is a first step in this direction. Our main result is to identify the correlation structure of the corrector, in dimension and higher. This correlation structure is similar to, but different from that of a Gaussian free field.
Cite
@article{arxiv.1402.1924,
title = {Correlation structure of the corrector in stochastic homogenization},
author = {Jean-Christophe Mourrat and Felix Otto},
journal= {arXiv preprint arXiv:1402.1924},
year = {2016}
}
Comments
Published at http://dx.doi.org/10.1214/15-AOP1045 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)