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

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Claeys, Tom [UCL] Olver, Sheehan [University of Sidney]

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.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2012
Language Anglais
Journal information "Contemporary Mathematics" - Vol. 578, no.Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications, p. 83-99 (2012)
Peer reviewed yes
Publisher American Mathematical Society
issn 0271-4132
e-issn 1098-3627
Publication status Publié
Affiliation UCL - SST/IRMP - Institut de recherche en mathématique et physique
Links
Bibliographic reference Claeys, Tom ; Olver, Sheehan. Numerical study of higher order analogues of the Tracy-Widom distribution. In: Contemporary Mathematics, Vol. 578, no.Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications, p. 83-99 (2012)
Permanent URL http://hdl.handle.net/2078/116957