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Numerical study of higher order analogues of the Tracy-Widom distribution
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.Comment: 17 pages, 7 figure