Subcritical multiplicative chaos and the characteristic polynomial of the Circular Beta Ensemble
Probability Seminar
8th November 2024, 3:30 pm – 4:30 pm
Fry Building, 2.04
We expand on the relationship between random matrix and Gaussian multiplicative chaos theories using the integrability properties of the circular beta-ensembles. We prove the convergence of powers of the modulus of the characteristic polynomial towards the multiplicative chaos throughout the subcritical phase, including some negative powers. This generalizes recent results proven in the unitary case (beta = 2) by Nikula, Saksman and Webb.
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