On the joint moments of the characteristic polynomials of random unitary matrices

Theo Assiotis, JONATHAN P. KEATING, JON WARREN

Research output: Working paper

Abstract

We establish the asymptotics of the joint moments of the characteristic polynomial of a random unitary matrix and its derivative for general real values of the exponents, proving a conjecture made by Hughes in 2001. Moreover, we give a probabilistic representation for the leading order coefficient in the asymptotic in terms of a real-valued random variable that plays an important role in the ergodic decomposition of the Hua-Pickrell measures. This enables us to establish connections between the characteristic function of this random variable and the σ-Painlevé III' equation.
Original languageEnglish
PublisherArXiv
Number of pages32
Publication statusPublished - 28 May 2020

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