Subcritical multiplicative chaos and the characteristic polynomial of the C$\beta$E

Gaultier Lambert; Joseph Najnudel

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arXiv · 2407.19817

Subcritical multiplicative chaos and the characteristic polynomial of the C$\beta$E

Gaultier Lambert·Joseph Najnudel

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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-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, [NSW20,BF22], to any beta>0 and for the eigenvalue counting field.

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Gaultier Lambert, Joseph Najnudel. 2024-07-29. Subcritical multiplicative chaos and the characteristic polynomial of the C$\beta$E. https://arxiv.org/abs/2407.19817

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