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Mixed moments of characteristic polynomials of random unitary matrices

Research output: Working paper

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Mixed moments of characteristic polynomials of random unitary matrices. / Bailey, Emma; Bettin, Sandro; Blower, Gordon et al.
2019.

Research output: Working paper

Harvard

Bailey, E, Bettin, S, Blower, G, Conrey, B, Prokhorov, A, Rubinstein, M & Snaith, N 2019 'Mixed moments of characteristic polynomials of random unitary matrices'.

APA

Bailey, E., Bettin, S., Blower, G., Conrey, B., Prokhorov, A., Rubinstein, M., & Snaith, N. (2019). Mixed moments of characteristic polynomials of random unitary matrices.

Vancouver

Bailey E, Bettin S, Blower G, Conrey B, Prokhorov A, Rubinstein M et al. Mixed moments of characteristic polynomials of random unitary matrices. 2019 Jan 12.

Author

Bailey, Emma ; Bettin, Sandro ; Blower, Gordon et al. / Mixed moments of characteristic polynomials of random unitary matrices. 2019.

Bibtex

@techreport{f636039c674846e2965d5317860caa31,
title = "Mixed moments of characteristic polynomials of random unitary matrices",
abstract = "Following the work of Conrey, Rubinstein and Snaith and Forrester and Witte 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 behaviour of moments of logarithmic derivatives of these characteristic polynomials evaluated near the unit circle. ",
keywords = "Random matrices, Zeta functions, Painleve differential equations",
author = "Emma Bailey and Sandro Bettin and Gordon Blower and Brian Conrey and Andrey Prokhorov and Michael Rubinstein and Nina Snaith",
year = "2019",
month = jan,
day = "12",
language = "English",
type = "WorkingPaper",

}

RIS

TY - UNPB

T1 - Mixed moments of characteristic polynomials of random unitary matrices

AU - Bailey, Emma

AU - Bettin, Sandro

AU - Blower, Gordon

AU - Conrey, Brian

AU - Prokhorov, Andrey

AU - Rubinstein, Michael

AU - Snaith, Nina

PY - 2019/1/12

Y1 - 2019/1/12

N2 - Following the work of Conrey, Rubinstein and Snaith and Forrester and Witte 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 behaviour of moments of logarithmic derivatives of these characteristic polynomials evaluated near the unit circle.

AB - Following the work of Conrey, Rubinstein and Snaith and Forrester and Witte 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 behaviour of moments of logarithmic derivatives of these characteristic polynomials evaluated near the unit circle.

KW - Random matrices

KW - Zeta functions

KW - Painleve differential equations

M3 - Working paper

BT - Mixed moments of characteristic polynomials of random unitary matrices

ER -