Speaker: Tuomo Kuusi

Title: Quantitative Stochastic Homogenization and Large-Scale Regularity

Abstract:

One of the principal difficulties in stochastic homogenization is 
transferring quantitative ergodic information from the coefficients 
to the solutions, since the latter are nonlocal functions of the former. 
In our recent book, jointly with S. Armstrong and J.-C. Mourrat, we have 
addressed this problem from a new perspective. Essentially, we use recently 
developed regularity theory for stochastic homogenization to accelerate 
the weak convergence of the energy density, flux and gradient of the 
solutions as we pass to larger and larger length scales, until it saturates 
at the CLT scaling. I will discuss our approach and give, at the same time, 
an informal introduction to our book.