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Mixed moments of characteristic polynomials of random unitary matrices

Research output: Contribution to journalArticle

Original languageEnglish
Article number083509
Number of pages27
JournalJournal of Mathematical Physics
Volume60
Issue number8
Early online date23 Aug 2019
DOIs
DateAccepted/In press - 3 Aug 2019
DateE-pub ahead of print - 23 Aug 2019
DatePublished (current) - 23 Aug 2019

Abstract

Following the work of Conrey, Rubinstein, and Snaith [Commun. Math. Phys. 267, 611 (2006)] and Forrester and Witte [J. Phys. A: Math. Gen. 39, 8983 (2006)], we examine a mixed moment of the characteristic polynomial and its derivative for matrices from the unitary group U(N) (also known as the CUE) and relate the moment to the solution of a Painlevé differential equation. We also calculate a simple form for the asymptotic behavior of moments of logarithmic derivatives of these characteristic polynomials evaluated near the unit circle.

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