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

  • Author(s): Tracy, Craig A.
  • Widom, Harold
  • et al.

Published Web Location

https://arxiv.org/pdf/solv-int/9707001.pdf
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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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