The ground state of a free Fermi gas is a classical example of determinantal processes whose correlation kernel is associated with a Schrödinger operator on R^n. This observation is due to Macchi (1975) and determinantal processes have been intensively studied since then. In this talk, I will explain how one proves universality of local correlations for these models using semiclassical analysis. If time permits, I will also mention a central limit theorem for a one-dimensional Fermi gas and explain the connection with random matrix theory. Joint work with Alix Deleporte.

Location: Zoom Meeting 
Meeting ID: 641 7966 7735
Passcode: 090135