Dr. Esteban Chavez (UCSB)

Title: Limit Theorems in Stochastic Homogenization

Abstract: Problems in stochastic homogenization typically deal with approximating solutions to PDEs with rapidly oscillatory random coefficients by solutions of homogenized deterministic PDEs. Even though many convergence results have been obtained in the form of a law of large numbers, very little is known about the rate of convergence or the large deviations of this approximation, especially in spatial dimensions greater than one. In this talk I will establish some analytic results concerning the rate of convergence and large deviations for some stochastic homogenization problems in higher spatial dimensions.