Hole probabilities and balayage of measures for planar Coulomb gases

by Christophe Charlier (Institut de recherche en mathématique et physique)

Tuesday 29 Oct 2024, 14:00 → 15:00 Europe/Brussels

B/2nd floor-B.203 - Seminar room (Marc de Hemptinne (chemin du Cyclotron, 2, Louvain-la-Neuve))

Coulomb gases consist of n particles repelling each other via the 2d Coulomb law and subject to the presence of an external potential. In this talk, I will discuss recent results on the probability that a given subset of the plane is free from particles when n is large. I will also talk about the most likely point configurations ("far from equilibrium") that produce such holes, which are described in terms of balayage measures.