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

Francesco Mezzadri; Alexi Reynolds; Brian Winn

doi:10.1088/1361-6544/aa518c

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

Francesco Mezzadri, Alexi Reynolds, Brian Winn

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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.

Original language	English
Article number	1034
Number of pages	25
Journal	Nonlinearity
Volume	30
Issue number	3
Early online date	2 Feb 2017
DOIs	https://doi.org/10.1088/1361-6544/aa518c
Publication status	Published - 2 Feb 2017

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Wegner estimates and universality for non-Hermitian matrices
Mezzadri, F.
1/05/14 → 31/10/17
Project: Research

Professor Francesco Mezzadri
- F.Mezzadribristol.acuk
- Probability, Analysis and Dynamics
- School of Mathematics - Professor of Mathematical Physics
- Applied Mathematics
- Mathematical Physics
Person: Academic , Member

Cite this

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

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Wegner estimates and universality for non-Hermitian matrices

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Professor Francesco Mezzadri

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