ar X iv : s ol v - in t / 9 70 70 01 v 1 2 7 Ju n 19 97 The Distribution of the Largest Eigenvalue in the Gaussian Ensembles
نویسندگان
چکیده
The focus of this survey paper is on the distribution function FNβ(t) for the largest eigenvalue in the finite N Gaussian Orthogonal Ensemble (GOE, β = 1), the Gaussian Unitary Ensemble (GUE, β = 2), and the Gaussian Symplectic Ensemble (GSE, β = 4) in the edge scaling limit of N → ∞. These limiting distribution functions are expressible in terms of a particular Painlevé II function. Comparisons are made with finite N simulations as well as a discussion of the universality of these distribution functions.
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