MATJ5102 Quantitative stochastic homogenization (JSS28), 2 op

NB! The application period for Jyväskylä Summer School courses is 1 March – 30 April. It is possible to sign up for the course until 1.8. but after the Summer School application deadline, admission to the course cannot be guaranteed.

The aim of the course is to describe some recent developments in random homogenization. The main focus is in linear elliptic equations with random coefficients. During the first part of the course we shall prove a quantitative rate of homogenization with very good stochastic integrability. Next, we will develop a stochastic regularity theory (where theories of De Giorgi and Stampacchia play crucial role) and finally use this regularity theory to accelerate the rate of convergence of homogenization, and to bootstrap it to the optimal one given by the Central Limit Theorem scaling.

To know what is meant by the stochastic homogenization. To be able to derive quantitative rate of homogenization for linear elliptic equations with random coefficients dealt in the course. Understand how regularity theory can be used to accelerate the rate of convergence.

Basic measure theory and stochastics. Sobolev spaces. Notion of distributional solution.  The course is based on the lecture notes "Quantitative stochastic homogenization and large-scale regularity" available at http://perso.ens-lyon.fr/jean-christophe.mourrat/lecturenotes.pdf

Obligatory attendance on lectures, and completing exercises.