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Discrete Tracy--Widom operators.

Research output: Contribution to journalJournal article

Published

Journal publication date10/2009
JournalProceedings of the Edinburgh Mathematical Society
Journal number3
Volume52
Number of pages15
Pages545-559
Original languageEnglish

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.

Bibliographic note

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.