PDEA Seminar: Fluctuations for a class of two-dimensional determinantal point processes

Abstract: I will introduce a family of two-dimensional determinantal point processes which generalize the Ginibre ensemble. These processes arise by considering the ground state of free fermions subject to a magnetic Schrödinger operator when the magnetic field is large. I will present a central limit theorem for linear statistics of such ensembles in the infinite number of particle limit. Like for the Ginibre ensemble, the fluctuations are of order one and there are contributions from both the bulk and boundary of the droplet. In contrast to the Ginibre ensemble, for anisotropic droplets, the contribution of the boundary is not conformally invariant. The proof relies on semiclassical method and the strong Szegő limit theorem. If I have time, I will mention analogous results for one-dimensional free fermions. Joint work with Alix Deleporte (Université Paris-Saclay).

This is a seminar in the PDEs and Applications seminar series.