Discrete Tracy–Widom operators
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Published:2009-09-23
Issue:3
Volume:52
Page:545-559
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ISSN:0013-0915
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Container-title:Proceedings of the Edinburgh Mathematical Society
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language:en
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Short-container-title:Proceedings of the Edinburgh Mathematical Society
Author:
Blower Gordon,McCafferty Andrew
Abstract
AbstractIntegrable 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.
Publisher
Cambridge University Press (CUP)
Subject
General Mathematics