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Gaultier Lambert: Statistical properties of free fermions

Time: Wed 2023-12-06 15.15 - 16.00

Location: Cramér room, Department of Mathematics, Albano

Participating: Gaultier Lambert (KTH)

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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.