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September 2016 Correlation structure of the corrector in stochastic homogenization
Jean-Christophe Mourrat, Felix Otto
Ann. Probab. 44(5): 3207-3233 (September 2016). DOI: 10.1214/15-AOP1045


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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Jean-Christophe Mourrat. Felix Otto. "Correlation structure of the corrector in stochastic homogenization." Ann. Probab. 44 (5) 3207 - 3233, September 2016.


Received: 1 February 2014; Revised: 1 January 2015; Published: September 2016
First available in Project Euclid: 21 September 2016

zbMATH: 1353.35040
MathSciNet: MR3551195
Digital Object Identifier: 10.1214/15-AOP1045

Primary: 35B27 , 35J15 , 35R60 , 82D30

Keywords: Homogenization‎ , Random media , two-point correlation function

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.44 • No. 5 • September 2016
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