Diffusion in the curl of the two-dimensional Gaussian Free Field

28.11.2022 16:15

I will discuss the large time behaviour of a Brownian diffusion in two dimensions, whose drift is divergence-free and ergodic, and given by the curl of the two-dimensional Gaussian Free Field.
Together with L. Haundschmid and F. Toninelli, we prove the conjecture by B. Tóth and B. Valkó that the mean square displacement is of order $t \sqrt{\log t}$. The same type of superdiffusive behaviour has been predicted to occur for a wide variety of (self)-interacting diffusions in dimension d = 2, including the diffusion of a tracer particle in a fluid, self-repelling polymers and random walks, Brownian particles in divergence-free random environments, and, more recently, the 2-dimensional critical Anisotropic KPZ equation.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Mathématique-Physique"

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