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arXiv · 1806.01831

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

Miika Nikula·Eero Saksman·Christian Webb
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Abstract

In this note 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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Miika Nikula, Eero Saksman, Christian Webb. 2018-06-05. Multiplicative chaos and the characteristic polynomial of the CUE: the $L^1$-phase. https://arxiv.org/abs/1806.01831

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