Multiplicative chaos for the characteristic polynomial of CβE

• Gaultier Lambert (KTH)

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).

Tracer and current fluctuations in 1D diffusive systems: integrability and beyond

• Aurélien Grabsch (CNRS (Sorbonne Université))

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.