Abstract:
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.
To the best of our knowledge, ours is the first instance in which $\sqrt{\log t}$ superdiffusion is rigorously established in this universality class.
Biography:
Giuseppe Cannizzaro is an Assistant Professor at the University of Warwick. Giuseppe got his PhD at Technische Universität Berlin in 2016 under the direction of Prof P. Friz. Subsequently, he joined the group of Prof. M. Hairer as postdoc at Imperial College London. After that, he moved to the University of Warwick, where he currently holds a position as Assistant Professor and EPSRC Fellow.
Giuseppe's work focuses on random interface models and their universality classes, statistical mechanics systems at criticality, stochastic analysis and singular stochastic PDEs.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai