Correlation structure of the corrector in stochastic homogenization

Jean-Christophe Mourrat and Felix Otto

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Submission date: 17. Feb. 2015
Pages: 23
published in: The annals of probability, 44 (2016) 5, p. 3207-3233 
DOI number (of the published article): 10.1214/15-AOP1045
Bibtex
MSC-Numbers: 35B27, 35J15, 35R60, 82D30
Keywords and phrases: homogenization, random media, two-point correlation function
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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 3 and higher. This correlation structure is similar to, but different from that of a Gaussian free field.