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

Research output: Contribution to journalArticle

Original languageEnglish
Article number1034
Number of pages24
JournalNonlinearity
Volume30
Issue number3
Early online date2 Feb 2017
DOIs
DateAccepted/In press - 5 Dec 2016
DateE-pub ahead of print - 2 Feb 2017
DatePublished (current) - Mar 2017

Abstract

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.

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    Rights statement: This is the final published version of the article (version of record). It first appeared online via IOP at http://iopscience.iop.org/article/10.1088/1361-6544/aa518c/meta. Please refer to any applicable terms of use of the publisher.

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