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.
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