PIICQ February 2025: Gaultier Lambert and Aurélien Grabsch

lundi 24 févr. 2025, 16:00 → 18:00 Europe/Paris

Zoom

The February 2025 online PIICQ meeting will take place on 24/02/2025 at 16:00 Paris time and we will listen to the talk of Gaultier Lambert (KTH) and to the talk of Aurélien Grabsch (CNRS, Sorbonne Université).

16:00 → 17:00 Multiplicative chaos for the characteristic polynomial of CβE¶

The goal of this talk is to explain how to use integrability of the circular β-ensembles (CβE) to derive the asymptotics of its characteristic polynomial. I will review the coupling for the CβE, in terms of orthogonal polynomials on the unit circle (OPUC), introduced by Killip and al. and use this framework to describe the asymptotics of powers of the characteristic polynomial (and the eigenvalue counting function) in terms of multiplicative chaos. I will also explain the relationship with previous results on the spectral measure of the corresponding CMV operator. This is joint work with Joseph Najnudel (University of Bristol).

Orateur: Gaultier Lambert (KTH)

17:00 → 18:00 Tracer and current fluctuations in 1D diffusive systems: integrability and beyond¶

In this talk, I will review recent results obtained on the symmetric simple exclusion process (SEP) and other models of 1D diffusive systems. At large scales, these models can be studied within the framework of macroscopic fluctuation theory (MFT). For a few models, like the SEP, the MFT equations are classically integrable and can be solved using the inverse scattering technique. However for most systems this is not the case, but several results can still be obtained in this case and signatures of non-integrability can be found.

Orateur: Aurélien Grabsch (CNRS (Sorbonne Université))