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MiS Preprint

Correlation structure of the corrector in stochastic homogenization

Jean-Christophe Mourrat and Felix Otto


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.

Feb 17, 2015
Feb 17, 2015
MSC Codes:
35B27, 35J15, 35R60, 82D30
homogenization, random media, two-point correlation function

Related publications

2016 Repository Open Access
Jean-Christophe Mourrat and Felix Otto

Correlation structure of the corrector in stochastic homogenization

In: The annals of probability, 44 (2016) 5, pp. 3207-3233