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Moments of the eigenvalue densities and of the secular coefficients of β-ensembles

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journal contribution
posted on 23.07.2018, 10:11 authored by Francesco Mezzadri, Alexi K. Reynolds, Brian WinnBrian Winn
© 2017 IOP Publishing Ltd & London Mathematical Society.We compute explicit formulae for the moments of the densities of the eigenvalues of the classical β-ensembles for finite matrix dimension as well as the expectation values of the coefficients of the characteristic polynomials. In particular, the moments are linear combinations of averages of Jack polynomials, whose coefficients are related to specific examples of Jack characters.

Funding

FM was partially supported by EPSRC research grant EP/L010305/1.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Nonlinearity

Volume

30

Issue

3

Pages

1034 - 1057

Citation

MEZZADRI, F., REYNOLDS, A.K. and WINN, B., 2017. Moments of the eigenvalue densities and of the secular coefficients of β-ensembles. Nonlinearity, 30(3), pp. 1034-1057.

Publisher

© 2017 IOP Publishing Ltd & London Mathematical Society

Version

VoR (Version of Record)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution 3.0 Unported (CC BY 3.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/by/3.0/

Acceptance date

05/12/2016

Publication date

2017

Notes

This is an Open Access Article. It is published by IOP under the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/

ISSN

0951-7715

eISSN

1361-6544

Language

en