Mathematikgebäude, Hörsaal E29

I will discuss the large-scale/ long-time behavior of a Brownian particle in a random, incompressible (divergence-free) vector field. If this vector field has correlations which decay sufficiently slowly, then the behavior of the particle is superdiffusive instead of diffusive. In particular, after time $t$, the particle will typically be a much larger distance than $\sqrt{t}$ from the origin. This phenomenon was explained in the physics literature in the late 1980s, using heuristic renormalization group arguments, as a divergence of effective diffusivity as we zoom out to large length scales. I will discuss recent mathematical innovations based on some analytic/PDE methods that allow us to make some of these renormalization group arguments rigorous.
​​​​​​​(This is joint work with A. Bou-Rabee and T. Kuusi.)

Mathematisches Kolloquium: Einblicke in die Wunder und Schönheit der Mathematik

Auch im Wintersemester 2025/2026 sind einige Vorträge im Mathematischen Kolloquium vorgesehen.
Sie finden jeweils am Mittwochnachmittag statt.

Vorab findet im Seminarraum E19 um 15.00 Uhr eine Einführung in das jeweilige Thema, insbesondere auch für Studierende, statt. Ab 15.30 Uhr gibt es einen 'Institutstee', ebenfalls im Seminarraum E19.

Scott Armstrong

Sorbonne Université, Paris