Lancaster EPrints

Discrete Tracy--Widom operators.

Blower, Gordon and McCafferty, Andrew (2009) Discrete Tracy--Widom operators. Proceedings of the Edinburgh Mathematical Society, 52 (3). pp. 545-559.

[img]
Preview
PDF (integrablepaper4.pdf)
Download (129Kb) | Preview
    [img]
    Preview
    PDF (download3.pdf)
    Download (181Kb) | Preview

      Abstract

      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.

      Item Type: Article
      Journal or Publication Title: Proceedings of the Edinburgh Mathematical Society
      Additional Information: 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.
      Uncontrolled Keywords: Hankel operators ; random matrices
      Subjects: Q Science > QA Mathematics
      Departments: Faculty of Science and Technology > Mathematics and Statistics
      ID Code: 1788
      Deposited By: Professor Gordon Blower
      Deposited On: 25 Feb 2008 08:51
      Refereed?: Yes
      Published?: Published
      Last Modified: 09 Oct 2013 13:12
      Identification Number:
      URI: http://eprints.lancs.ac.uk/id/eprint/1788

      Actions (login required)

      View Item