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

## 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

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:

/dk/atira/pure/subjectarea/asjc/2600/2600

Subjects:

?? hankel operatorsrandom matricesgeneral mathematicsmathematics(all)qa mathematics ??

Departments:

ID Code:

1788

Deposited By:

Deposited On:

25 Feb 2008 08:51

Refereed?:

Yes

Published?:

Published

Last Modified:

10 Sep 2024 00:07