Correlation structure of the corrector in stochastic homogenization

• Jean-Christophe Mourrat ^[2] ; Felix Otto ^[1]
  1. [1] Max Planck Institute for Mathematics in the Sciences

     Max Planck Institute for Mathematics in the Sciences

     Kreisfreie Stadt Leipzig, Alemania

     
  2. [2] CNRS
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 5, 2016, págs. 3207-3233
• Idioma: inglés
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• Resumen

  • 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 33 and higher. This correlation structure is similar to, but different from that of a Gaussian free field.