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Discrete Tracy–Widom operators

Published online by Cambridge University Press:  23 September 2009

Gordon Blower
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK; Email: ([email protected], [email protected])
Andrew McCafferty
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK; Email: ([email protected], [email protected])
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Abstract

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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. 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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2009