Correlation structure of the corrector in stochastic homogenization

Jean Christophe Mourrat, Felix Otto

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)3207-3233
Number of pages27
JournalAnnals of Probability
Issue number5
StatePublished - 2016


  • Homogenization
  • Random media
  • Two-point correlation function

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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