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We study a family of distributions that arise in critical unitary randommatrix ensembles. They are expressed as Fredholm determinants and describe thelimiting distribution of the largest eigenvalue when the dimension of therandom matrices tends to infinity. The family contains the Tracy-Widomdistribution and higher order analogues of it. We compute the distributionsnumerically by solving a Riemann-Hilbert problem numerically, plot thedistributions, and discuss several properties that they appear to exhibit.

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