Journal
ANNALS OF PROBABILITY
Volume 44, Issue 5, Pages 3207-3233Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/15-AOP1045
Keywords
Homogenization; random media; two-point correlation function
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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.
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