Winn_Mezzadri_2017_Nonlinearity_30_1034.pdf (1.2 MB)
Moments of the eigenvalue densities and of the secular coefficients of β-ensembles
journal contribution
posted on 2018-07-23, 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
NonlinearityVolume
30Issue
3Pages
1034 - 1057Citation
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 SocietyVersion
- 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
2016-12-05Publication date
2017Notes
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
0951-7715eISSN
1361-6544Publisher version
Language
- en
