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Discrete Tracy--Widom operators.

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<mark>Journal publication date</mark>10/2009
<mark>Journal</mark>Proceedings of the Edinburgh Mathematical Society
Issue number3
Number of pages15
Pages (from-to)545-559
Publication StatusPublished
<mark>Original language</mark>English


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.