Moments of the logarithmic derivative of characteristic polynomials from SO(2N) and USp(2N)

Emilia Alvarez; Nina C Snaith

doi:10.1063/5.0008423

Moments of the logarithmic derivative of characteristic polynomials from SO(2N) and USp(2N)

Emilia Alvarez^*, Nina C Snaith^*

^*Corresponding author for this work

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Abstract

We study moments of the logarithmic derivative of characteristic polynomials of orthogonal and symplectic random matrices. In particular, we compute the asymptotics for large matrix size, N, of these moments evaluated at points which are approaching 1. This follows work of Bailey, Bettin, Blower, Conrey, Prokhorov, Rubinstein and Snaith where they compute these asymptotics in the case of unitary random matrices.

Original language	English
Article number	103506 (2020)
Journal	Journal of Mathematical Physics
Volume	61
Early online date	8 Oct 2020
DOIs	https://doi.org/10.1063/5.0008423 https://doi.org/10.1063/5.0008423
Publication status	E-pub ahead of print - 8 Oct 2020

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Professor Nina C Snaith
- N.C.Snaithbristol.acuk
- School of Mathematics - Professor of Mathematical Physics
- Applied Mathematics
- Mathematical Physics
- Pure Mathematics
Person: Academic , Member

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title = "Moments of the logarithmic derivative of characteristic polynomials from SO(2N) and USp(2N)",

abstract = "We study moments of the logarithmic derivative of characteristic polynomials of orthogonal and symplectic random matrices. In particular, we compute the asymptotics for large matrix size, N, of these moments evaluated at points which are approaching 1. This follows work of Bailey, Bettin, Blower, Conrey, Prokhorov, Rubinstein and Snaith where they compute these asymptotics in the case of unitary random matrices. ",

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AU - Snaith, Nina C

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N2 - We study moments of the logarithmic derivative of characteristic polynomials of orthogonal and symplectic random matrices. In particular, we compute the asymptotics for large matrix size, N, of these moments evaluated at points which are approaching 1. This follows work of Bailey, Bettin, Blower, Conrey, Prokhorov, Rubinstein and Snaith where they compute these asymptotics in the case of unitary random matrices.

AB - We study moments of the logarithmic derivative of characteristic polynomials of orthogonal and symplectic random matrices. In particular, we compute the asymptotics for large matrix size, N, of these moments evaluated at points which are approaching 1. This follows work of Bailey, Bettin, Blower, Conrey, Prokhorov, Rubinstein and Snaith where they compute these asymptotics in the case of unitary random matrices.

U2 - 10.1063/5.0008423

DO - 10.1063/5.0008423

M3 - Article (Academic Journal)

VL - 61

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

M1 - 103506 (2020)

ER -

Moments of the logarithmic derivative of characteristic polynomials from SO(2N) and USp(2N)

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Professor Nina C Snaith

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