Fluctuations in stochastic homogenization

Jeudi 13 juin 14:00-15:00 - Mitia Duerinckx - ENS de Lyon

Résumé : In this talk, we review recent developments on large-scale fluctuations of the solution operator for a uniformly elliptic PDE in divergence form with random coefficients. We focus for simplicity on Gaussian-type coefficients and make strong use of Malliavin calculus. We establish a general pathwise theory of fluctuations based on the new key notion of homogenization commutator. We further investigate the effect of strongly correlated coefficients, study possible degeneracy issues for the limit, and show how the theory can be extended to optimally describe higher-order fluctuations in terms of suitable higher-order commutators.

Lieu : IMO, Salle 3L8

Fluctuations in stochastic homogenization  Version PDF