The Distribution of the Largest Eigenvalue in the Gaussian Ensembles
Craig A. Tracy, Harold Widom
Abstract
The focus of this survey paper is on the distribution function for the largest eigenvalue in the finite N Gaussian ensembles (GOE,GUE,GSE) in the edge scaling limit of N->infinity. These limiting distribution functions are expressible in terms of a particular Painleve 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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