Numerical study of higher order analogues of the Tracy-Widom distribution

Claeys, Tom;Olver, Sheehan
(2012) Contemporary Mathematics — Vol. 578, n° Recent Advances in Orthogonal Polynomials, p. 83-99 (2012)

Files

manuscriptClaeysOlver-CONM-v2.pdf
  • Restricted Access
  • Adobe PDF
  • 758.18 KB
Request a copy

Details

Authors
  • Claeys, Tomorcid-logoUCLouvain
    Author
  • Olver, SheehanUniversity of Sidney
    Author
Abstract
We study a family of distributions that arise in critical unitary random matrix ensembles. They are expressed as Fredholm determinants and describe the limiting distribution of the largest eigenvalue when the dimension of the random matrices tends to infinity. The family contains the Tracy-Widom distribution and higher order analogues of it. We compute the distributions numerically by solving a Riemann-Hilbert problem numerically, plot the distributions, and discuss several properties that they appear to exhibit.
Affiliations

Citations

  • APA
  • Chicago
  • FWB

Claeys, T., & Olver, S. (2012). Numerical study of higher order analogues of the Tracy-Widom distribution. Contemporary Mathematics, 578(Recent Advances in Orthogonal Polynomials), 83-99. https://doi.org/10.1090/conm/578 (Original work published 2012)