Multiplicative chaos and the characteristic polynomial of the CUE: The 𝐿¹-phase

Nikula, Miika; Saksman, Eero; Webb, Christian

doi:10.1090/tran/8020

Multiplicative chaos and the characteristic polynomial of the CUE: The $L^1$-phase
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by Miika Nikula, Eero Saksman and Christian Webb PDF

Trans. Amer. Math. Soc. 373 (2020), 3905-3965 Request permission

Abstract:

In this article we prove that suitable positive powers of the absolute value of the characteristic polynomial of a Haar distributed random unitary matrix converge in law, as the size of the matrix tends to infinity, to a Gaussian multiplicative chaos measure once correctly normalized. We prove this in the whole $L^1$- or subcritical phase of the chaos measure.

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