The Annals of Probability
- Ann. Probab.
- Volume 44, Number 5 (2016), 3207-3233.
Correlation structure of the corrector in stochastic homogenization
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.
Ann. Probab., Volume 44, Number 5 (2016), 3207-3233.
Received: February 2014
Revised: January 2015
First available in Project Euclid: 21 September 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35B27: Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50] 35J15: Second-order elliptic equations 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 82D30: Random media, disordered materials (including liquid crystals and spin glasses)
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