Scaling limits of fluctuations in stochastic homogenization (Yu Gu - Stanford University)

Equations with small scales abound in physics and applied science. When the coefficients vary on microscopic scales, the local fluctuations average out under certain assumptions and we have the so-called homogenization phenomenon. In this talk, I will try to explain some probabilistic approaches we use to obtain the first order random fluctuations in stochastic homogenization. If homogenization is to be viewed as a law of large number type result, here we are looking for a central limit theorem. The tools we use include the Kipnis-Varadhan's method, a quantitative martingale central limit theorem and the Stein's method. Based on joint work with Jean-Christophe Mourrat.