Limit Theorems for Differential Equations in Random Media

Problems in stochastic homogenization theory typically deal with approximating dierential operators with rapidly oscillatory random coefficients by operators with homogenized deterministic coefficients. Even though the convergence of these operators in multiple scales is well-studied in the existing literature in the form of a Law of Large Numbers, very little is known about their rate of convergence or their large deviations. This work establishes analytic results for the Gaussian correction in homogenization, and large deviation results for homogenization problems in random media. Several special cases are analyzed in detail.