Vortrag im Rahmen des Forschungsseminars Analysis[21.01.2020]
Im Rahmen des Forschungsseminars Analysis hält am Dienstag, den 21.01.2020, um15:00 Uhr, Herr Dr. Matthias Erbar (Universität Bonn) einen Vortrag zum Thema:
A variational characterization of the Sineβ point process.
Der Vortrag findet im Raum E 408, Universitätsstraße 1/11 (Gebäude 3), statt. Interessierte sind herzlich eingeladen.
Abstract: The one-dimensional log gas in finite volume is a system of particles interacting via a repul- sive logarithmic potential and confined by some external field. When the number of particles goes to infinity, their macroscopic empirical distribution approaches a deterministic limit shape. When zooming in one sees microscopic fluctuations around this limit which are described in the limit by a stationary point process, the Sineβ process constructed by Valko and Virag. Leblé and Serfaty have established a large deviation principle for the microscopic configurations governed by a rate function which is the sum of a specific entropy and a renormalized interaction energy. Thus the typical microscopic behavior of the gas is described by the minimizers of this free energy functional, one of which is the Sineβ pro- cess. We show that this is indeed the unique minimizer. Our argument is based on optimal transport of random point configurations and exploits strict displacement convexity in the free energy functional.