Workshop: Subcritical multiplicative chaos and the characteristic polynomial of the CBE

Speaker
Najnudel, Bristol University


Abstract
We expand on the relationship between random matrix and multiplicative chaos theories using the integrability properties of the circular beta-ensembles. We give a comprehensive proof of the multiplicative chaos convergence for the characteristic polynomial and eigenvalue counting function of the circular beta-ensembles throughout the subcritical phase, including negative powers. This generalizes recent results in the unitary case to any beta>0 and for the eigenvalue counting field.