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The Distribution of the Largest Eigenvalue in the Gaussian Ensembles

solv-int 2008-02-03 v1 Mathematical Physics math.MP Exactly Solvable and Integrable Systems

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.

Keywords

Cite

@article{arxiv.solv-int/9707001,
  title  = {The Distribution of the Largest Eigenvalue in the Gaussian Ensembles},
  author = {Craig A. Tracy and Harold Widom},
  journal= {arXiv preprint arXiv:solv-int/9707001},
  year   = {2008}
}

Comments

13 pages