The Distribution of the Largest Eigenvalue in the Gaussian Ensembles

Details The Distribution of the Largest Eigenvalue in the Gaussian Ensembles The Distribution of the Largest Eigenvalue in the Gaussian Ensembles

1997-06-27

arxiv.org/abs/solv-int/9707001v1

in Calogero-Moser-Sutherland Models, eds. J.F. van Diejen and L. Vinet, CRM Series in Mathematical Physics 4, Springer-Verlag,

Physics

Mathematical Physics

13 pages

Scientific paper

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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