The Distribution of the Largest Eigenvalue in the Gaussian Ensembles

Craig A. Tracy; Harold Widom

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The Distribution of the Largest Eigenvalue in the Gaussian Ensembles

Craig A. Tracy·Harold Widom

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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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BibTeX RIS

Craig A. Tracy, Harold Widom. 1997-06-27. The Distribution of the Largest Eigenvalue in the Gaussian Ensembles. https://arxiv.org/abs/solv-int/9707001

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