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

doi:10.1063/1.5092780

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 journal › Article (Academic Journal) › peer-review

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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 language	English
Article number	083509
Number of pages	27
Journal	Journal of Mathematical Physics
Volume	60
Issue number	8
Early online date	23 Aug 2019
DOIs	https://doi.org/10.1063/1.5092780
Publication status	Published - 23 Aug 2019

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title = "Mixed moments of characteristic polynomials of random unitary matrices",

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 Painlev{\'e} 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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T1 - Mixed moments of characteristic polynomials of random unitary matrices

AU - Bailey, E. C.

AU - Bettin, S.

AU - Blower, G.

AU - Conrey, J. B.

AU - Prokhorov, A.

AU - Rubinstein, M. O.

AU - Snaith, N. C.

PY - 2019/8/23

Y1 - 2019/8/23

N2 - 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.

AB - 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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DO - 10.1063/1.5092780

M3 - Article (Academic Journal)

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SN - 0022-2488

VL - 60

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 8

M1 - 083509

ER -

Mixed moments of characteristic polynomials of random unitary matrices

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Dr Emma C Bailey

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Mixed moments of characteristic polynomials of random unitary matrices

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Dr Emma C Bailey

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