Yacin Ameur: The Coulomb gas near a spectral outpost

Abstract:

We consider two-dimensional Coulomb systems in the regime when the droplet is connected, while the coincidence set for the obstacle problem contains an analytic Jordan curve outside of the droplet. A nontrivial (Heine-distributed) number of particles will tend to fall in the vicinity of this curve, which we denote “spectral outpost”. Under the process of Laplacian growth, the outpost grows into a new ring-shaped component of the droplet, and the study of outposts is therefore closely related to the regime of disconnected droplets. We study among other things fluctuations of linear statistics. The talk is based on joint works with Joakim Cronvall and Christophe Charlier.