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

2018/06/05 by Miika Nikula, Nikula, Miika, Eero Saksman +4 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1806.01831

openalex publication_date 2018/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we prove that suitable positive powers of the absolute value of\nthe characteristic polynomial of a Haar distributed random unitary matrix\nconverge in law, as the size of the matrix tends to infinity, to a Gaussian\nmultiplicative chaos measure once correctly normalized. We prove this in the\nwhole L¹- or subcritical phase of the chaos measure.\n

Citations

• Integrability of Liouville theory: proof of the DOZZ Formula

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