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Probabilistic approaches to quantitative stochastic homogenizationPDE 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.