Speaker: Tuomo Kuusi
Title: Superdiffusion for Brownian motion with incompressible random drift and quantitative homogenization in high contrast
 
Abstract: We consider the long-time behavior of a diffusion process on~$\mathbb{R}^d$ advected by a stationary random vector field, which is assumed to be divergence-free, dihedrally symmetric in law, and have a log-correlated potential. A particular case is $\nabla^\perp$ of the Gaussian free field in two dimensions. We show that the system has quenched superdiffusive scaling. I will also discuss some recent and ongoing work on the theory of high-contrast homogenization. In the process, we have developed a renormalization procedure, which is expected to have applications in mathematical physics beyond this setting.