The Widom-Dyson constant for the gap probability in random matrix theory

P. Deift, A. Its, I. Krasovsky, X. Zhou

Research output: Contribution to journalArticle

Abstract

In the bulk scaling limit for the Gaussian Unitary Ensemble in random matrix theory, the probability that there are no eigenvalues in the interval (0, 2 s) is given by Ps = det (I - Ks), where Ks is the trace-class operator with kernel Ks (x, y) = frac(sin (x - y), π (x - y)) acting on L2 (0, 2 s). In the analysis of the asymptotic behavior of Ps as s → ∞, there is particular interest in the constant term known as the Widom-Dyson constant. We present a new derivation of this constant, which can be adapted to calculate similar critical constants in other problems arising in random matrix theory.

Original languageEnglish (US)
Pages (from-to)26-47
Number of pages22
JournalJournal of Computational and Applied Mathematics
Volume202
Issue number1 SPECIAL ISSUE
DOIs
StatePublished - May 1 2007

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Keywords

  • Asymptotic expansions
  • Correlation functions
  • Random matrices
  • Riemann-Hilbert problem

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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