Blower, Gordon and McCafferty, Andrew (2009) *Discrete Tracy--Widom operators.* Proceedings of the Edinburgh Mathematical Society, 52 (3). pp. 545-559. ISSN 1464-3839

Official URL: http://dx.doi.org/10.1017/S001309150700140X

## Abstract

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. This paper considers discrete Tracy--Widom operators, and gives 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 equatio and the Fourier transform of Mathieu's equation.

Item Type: | Journal Article |
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Journal or Publication Title: | Proceedings of the Edinburgh Mathematical Society |

Additional Information: | AMS 2000 classification: 47B35 http://journals.cambridge.org/action/displayJournal?jid=PEM The final, definitive version of this article has been published in the Journal, Proceedings of the Edinburgh Mathematical Society, 52 (3), pp 545-559 2009, © 2009 Cambridge University Press. |

Uncontrolled Keywords: | Hankel operators ; random matrices |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 1788 |

Deposited By: | Professor Gordon Blower |

Deposited On: | 25 Feb 2008 08:51 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 23 Feb 2018 03:39 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/1788 |

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