Correlation structure of the corrector in stochastic homogenization
Jean-Christophe Mourrat and Felix Otto
Contact the author: Please use for correspondence this email.
Submission date: 17. Feb. 2015
published in: The annals of probability, 44 (2016) 5, p. 3207-3233
DOI number (of the published article): 10.1214/15-AOP1045
MSC-Numbers: 35B27, 35J15, 35R60, 82D30
Keywords and phrases: homogenization, random media, two-point correlation function
Download full preprint: PDF (569 kB)
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 3 and higher. This correlation structure is similar to, but different from that of a Gaussian free field.