Speaker: Jean-Christophe Mourrat

Title: 

Describing fluctuations in stochastic homogenization

Abstract:

Consider the solution of a divergence-form problem with random
coefficients. Under suitable assumptions on the law of the coefficients,
homogenisation theory ensures that as the correlation length of the
random coefficients is sent to 0, this solution converges to the
solution of a similar problem with constant, ”homogenised” coefficients.
The problem of quantifying the error in this convergence has witnessed
tremendous progress recently. The goal of this talk is to explain how
one can go beyond error bounds, and describe precisely the statistics of
the fluctuations in terms of a finite number of new effective parameters.