CORRELATION STRUCTURE OF THE CORRECTOR IN STOCHASTIC HOMOGENIZATION

• 成果类型: Article
• 署名作者: Mourrat, Jean-Christophe; Otto, Felix
• 署名单位: Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); Max Planck Society
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1045
• 发表日期: 2016
• 页码: 3207-3233
• 关键词: elliptic-equations; parabolic equations; strong-convergence; Scaling Limit; approximation; fluctuations; coefficients; expansion; models

摘要

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.