arXiv:1402.1924 Abstract | arXiv Analytics

arXiv:1402.1924 [math.AP]Abstract References Reviews Resources

Correlation structure of the corrector in stochastic homogenization

Published 2014-02-09, updated 2015-02-15Version 2

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.

Comments: 21 pages. V2: minor modifications

Categories: math.AP, math.PR

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

Keywords: correlation structure, stochastic homogenization, gaussian free field, error bounds, precise descriptions

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