Title:
Outliers in Coulomb-type particle systems


Abstract:
We consider particle systems (≡ point processes) in the plane, characterized by a large number of outliers away from a droplet, where the bulk of the particles accumulate in the many-particle limit. For two different types of such systems, we observe that the limiting outlier process essentially only depends on the shape of the component in the complement of the droplet containing them. Moreover, the outliers in different such components are asymptotically independent, and exhibit conformal invariance with respect to the shape of the component.

The behavior of the particle systems we study is tied to certain reproducing kernel Hilbert spaces.
Our method is based on proving convergence of appropriate kernels to universal limits (certain weighted Bergman and Szegő kernels).
I will explain the (little) probabilistic background needed for the talk.
Based on a joint work with R. Butez, D. García-Zelada, and A. Wennman (see the preliminary version: arXiv:2104.03959).