Subcritical multiplicative chaos and the characteristic polynomial of the C$$\beta $$E
Abstract
Abstract The goal of this article is to expand on the relationship between random matrix and multiplicative chaos theories using the integrability properties of the circular $$\beta $$ β -ensembles. We obtain the multiplicative chaos convergence for the characteristic polynomial and eigenvalue counting function of the circular $$\beta $$ β -ensembles throughout the subcritical phase, including negative powers. This generalizes recent results in the unitary case, [8, 40], to any $$\beta >0$$ β > 0 and for the eigenvalue counting field.
Fields of Study & Subjects
Quantum chaos and dynamical systems
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- Probability Theory and Related Fields
- Publisher
- Springer Science and Business Media LLC
- Volume
- 196
- Issue
- 3-4
- Pages
- 2103-2154
- Publication date
- 28 May 2026
- Language
- EN