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
DOI: 10.1214/15-AOP1045
Enlaces
- Texto completo
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.