Department of Mathematics
The Distribution of the Largest Eigenvalue in the Gaussian Ensembles
- Author(s): Tracy, Craig A.
- Widom, Harold
- et al.
Published Web Locationhttps://arxiv.org/pdf/solv-int/9707001.pdf
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.