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

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 po...

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Bibliographic Details
Published in:Nonlinearity 2017-03, Vol.30 (3), p.1034-1057
Main Authors: Mezzadri, Francesco, Reynolds, Alexi K, Winn, Brian
Format: Article
Language:English
Subjects:
ensembles
Jack characters
Jack polynomials
multivariate orthogonal polynomials
random matrix theory
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Summary: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.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/aa518c