2014/02/28 by Jean-Christophe Mourrat, Felix Otto, Félix Otto · 51 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Composite Material Mechanics #Gaussian #Gaussian free field #Homogenization (climate) #Mathematical analysis #Mathematics #Predictor–corrector method #Randomness #Statistical physics #Statistics #math.AP #math.PR
paper · pdf · doi:10.1214/15-aop1045
published in The Annals of Probability 44(5) (Institute of Mathematical Statistics) · Published at http://dx.doi.org/10.1214/15-AOP1045 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2016/09/01 · arxiv created 2016/09/28 · arxiv updated 2016/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.