Bálint Tóth: Random walk in doubly stochastic random environment-diffusive and super-diffusive limits

Speaker: Bálint Tóth

Title: Random walk in doubly stochastic random environment-diffusive and super-diffusive limits 

Abstract:  I will give a survey from a bird's-eye-view of the problem of scaling limit for random walks (or diffusions) in divergence-free random drift field, with explicit examples. The relevance/motivation of the problem is manifold. In particular, it models diffusion of particles suspended in incompressible turbulent flow - a question of undoubted physical relevance. The main results state (1) diffusive scaling limit under the infamous H_{-1} condition (to be explained), and (2) superdiffusive (i.e. faster-than-normal spreading) in some typical cases when the H_{-1} condition fails. I will highlight some elements of the proofs, like extension of Nash's moment bound and down-to-earth (non-abstract) functional analytic approaches.