Speaker: Yu Gu, Stanford University.
Title: A two-scale expansion for equations with random coefficients: a probabilistic approach

ABSTRACT: Recently, quantitative stochastic homogenization of operators in divergence form has witnessed important progress, starting from the work of Gloria and Otto. Our goal is to go beyond the error bound and further analyze the statistical fluctuations around the homogenized limit. Using a probabilistic representation, the Kipnis-Varadhan method applied to diffusion in random environment, and a quantitative martingale central limit theorem, we prove a pointwise two-scale expansion by a stationary corrector. This is joint work with Jean-Christophe Mourrat.