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Probabilistic approaches to quantitative stochastic homogenization

PDE and Applied Math Seminar

Speaker: Yu Gu, Stanford U
Location: 1147 MSB
Start time: Mon, Apr 27 2015, 4:10PM

Quantitative stochastic homogenization of operators in divergence form has witnessed important progress recently. Our goal is to go beyond the error bound to analyze statistical fluctuations around the homogenized limit. We prove a pointwise two-scale expansion and a large scale central limit theorem for the solution. The approach is probabilistic. The main ingredients include the Kipnis-Varadhan method applied to symmetric diffusion in random environment, a quantitative martingale central limit theorem, the Helffer-Sjostrand covariance representation and Stein's method. This is joint work with Jean-Christophe Mourrat.