Correlation structure of the corrector in stochastic homogenization

Jean-Christophe Mourrat (1) , Felix Otto (2)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 MPI-MiS - Max-Planck-Institut für Mathematik in den Naturwissenschaften

Recently, the quantification of errors in the stochastic homoge-nization 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.

Mots clés: homogenization; random media; two-point correlation function

Domaines: Equations aux dérivées partielles [math.AP]

Jean-Christophe Mourrat, Felix Otto. Correlation structure of the corrector in stochastic homogenization. Annals of Probability, 2016, 44, pp.3207 - 3233. ⟨10.1214/15-AOP1045⟩. ⟨ensl-01401887⟩