Gaultier Lambert: Statistical properties of free fermions
Tid: On 2023-12-06 kl 15.15 - 16.00
Plats: Cramér room, Department of Mathematics, Albano
Medverkande: Gaultier Lambert (KTH)
Abstract
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 \(\mathbb{R}^n\). This observation is due to Macchi (1975) and determinantal processes have been intensively studied since then. In this talk, I will report on recent results that we obtained jointly with Alix Deleporte (Université Paris-Saclay) and Sylvain Chabredier describing the fluctuations of these determinantal processes using techniques from semiclassical analysis.
I will first explain the model and how to obtain universality of local correlations for these models. Then, if time permits, I will present a central limit theorem valid for linear statistics of generic one-dimensional Fermi gas, as well as an analogous result for the \(n\)-dimensional.