Multiplicative chaos and the characteristic polynomial of the CUE: The L^1-phase

Multiplicative chaos and the characteristic polynomial of the CUE: The L^1-phase

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...

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Veröffentlicht in:Transactions of the American Mathematical Society 2020-06, Vol.373 (6), p.3905
Hauptverfasser: Miika Nikula, Eero Saksman, Christian Webb
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Eero Saksman
Christian Webb
description 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.
doi_str_mv 10.1090/tran/8020
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title Multiplicative chaos and the characteristic polynomial of the CUE: The L^1-phase
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