Correlation structure of the corrector in stochastic homogenization

Abstract : Recently, the quantification of errors in the stochastic homoge-nization 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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Submitted on : Wednesday, November 23, 2016 - 10:22:47 PM
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Jean-Christophe Mourrat, Felix Otto. Correlation structure of the corrector in stochastic homogenization. Annals of Probability, Institute of Mathematical Statistics, 2016, 44, pp.3207 - 3233. 〈10.1214/15-AOP1045〉. 〈ensl-01401887〉

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