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

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

2011-11-15

arxiv.org/abs/1111.3527v1

Physics

Mathematical Physics

17 pages, 7 figures

Scientific paper

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.

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