## The Annals of Probability

### Correlation structure of the corrector in stochastic homogenization

#### 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.

#### Article information

Source
Ann. Probab., Volume 44, Number 5 (2016), 3207-3233.

Dates
Revised: January 2015
First available in Project Euclid: 21 September 2016

https://projecteuclid.org/euclid.aop/1474462096

Digital Object Identifier
doi:10.1214/15-AOP1045

Mathematical Reviews number (MathSciNet)
MR3551195

Zentralblatt MATH identifier
1353.35040

#### Citation

Mourrat, Jean-Christophe; Otto, Felix. Correlation structure of the corrector in stochastic homogenization. Ann. Probab. 44 (2016), no. 5, 3207--3233. doi:10.1214/15-AOP1045. https://projecteuclid.org/euclid.aop/1474462096

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