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Discrete Tracy–Widom operators

Part of: Special classes of linear operators

Published online by Cambridge University Press:  23 September 2009

Gordon Blower  and
Andrew McCafferty
Gordon Blower
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK; Email: (g.blower@lancaster.ac.uk, a.mccafferty@lancaster.ac.uk)
Andrew McCafferty
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK; Email: (g.blower@lancaster.ac.uk, a.mccafferty@lancaster.ac.uk)
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Abstract

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Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large self-adjoint random matrices from the generalized unitary ensembles. We consider discrete Tracy–Widom operators and give sufficient conditions for a discrete integrable operator to be the square of a Hankel matrix. Examples include the discrete Bessel kernel and kernels arising from the almost Mathieu equation and the Fourier transform of Mathieu's equation.

Keywords

Hankel operatorsrandom matricesAnderson localization

MSC classification

Secondary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 3 , October 2009 , pp. 545 - 559
Copyright
Copyright © Edinburgh Mathematical Society 2009