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Correlation structure of the corrector in stochastic homogenization
Jean-Christophe Mourrat and Felix OttoAbstract
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.
- Received:
- 17.02.15
- Published:
- 17.02.15
- MSC Codes:
- 35B27, 35J15, 35R60, 82D30
- Keywords:
- homogenization, random media, two-point correlation function