Discrete TracyWidom Operators
Abstract
Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large selfadjoint random matrices from the generalized unitary ensembles. This paper considers discrete TracyWidom 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2008
 DOI:
 10.48550/arXiv.0806.4919
 arXiv:
 arXiv:0806.4919
 Bibcode:
 2008arXiv0806.4919B
 Keywords:

 Mathematics  Functional Analysis;
 47B35
 EPrint:
 16 pages