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F. Toninelli:
"Diffusion in the curl of the 2-dimensional Gaussian Free Field";
Vortrag: Bristol, Queen Mary, and Warwick Probability Seminar, Warwick (eingeladen); 17.11.2021.

I will discuss the large time behaviour of a Brownian diffusion in two dimensions, whose drift is divergence−free, ergodic and given by the curl of the 2−dimensional Gaussian Free Field. Together with G. Cannizzaro and L. Haundschmid, we prove the conjecture by B. Toth and B. Valko that the mean square displacement is of order t√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: 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 authors´ knowledge, ours is the first instance in which √log t superdiffusion is rigorously established in this universality class.