Multiplicative chaos and the characteristic polynomial of the CUE: the \(L^1\)-phase. (English) Zbl 1441.60008
Summary: 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.
MSC:
| 60B20 | Random matrices (probabilistic aspects) |
| 15B05 | Toeplitz, Cauchy, and related matrices |
| 60G57 | Random measures |
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