Mixed moments of characteristic polynomials of random unitary matrices

E. C. Bailey*, S. Bettin, G. Blower, J. B. Conrey, A. Prokhorov, M. O. Rubinstein, N. C. Snaith

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

2 Citations (Scopus)
1 Downloads (Pure)

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.

Original languageEnglish
Article number083509
Number of pages27
JournalJournal of Mathematical Physics
Volume60
Issue number8
Early online date23 Aug 2019
DOIs
Publication statusPublished - 23 Aug 2019

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