30. Sep 2021

Diffusion in the curl of the 2-dimensional Gaussian Free Field

VIENNA PROBABILITY SEMINAR

Datum: 30. September 2021 | 16:30 – 17:20
Sprecher: Fabio Toninelli, TU Vienna
Veranstaltungsort: Rényi Institute Budapest

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 $t \sqrt{\log t}$. The same type of superdiffusive behaviour has been predicted to occur for a wide variety of (self)-interacting diffusions in dimension d = 2: 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 $\sqrt{\log t}$ superdiffusion is rigorously established in this universality class.

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Datum:
30. September 2021
16:30 – 17:20

Sprecher:
Fabio Toninelli, TU Vienna

Veranstaltungsort:
Rényi Institute Budapest

Ansprechpartner:

Birgit Oosthuizen-Noczil

Email:
birgit.oosthuizen-noczil@ist.ac.at

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