Mixed moments of characteristic polynomials of random unitary matrices

Mixed moments of characteristic polynomials of random unitary matrices

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)...

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Veröffentlicht in:Journal of mathematical physics 2019-08, Vol.60 (8)
Hauptverfasser: Bailey, E. C., Bettin, S., Blower, G., Conrey, J. B., Prokhorov, A., Rubinstein, M. O., Snaith, N. C.
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic properties
Differential equations
Mathematical analysis
Physics
Polynomials
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Zusammenfassung: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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.5092780