Discrete Tracy-Widom Operators

Details Discrete Tracy-Widom Operators Discrete Tracy-Widom Operators

2008-06-30

arxiv.org/abs/0806.4919v1

Mathematics

Functional Analysis

16 pages

Scientific paper

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 equation and the Fourier transform of Mathieu's equation.

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