
Statistics Papers
Document Type
Journal Article
Date of this Version
2012
Publication Source
The Annals of Applied Probability
Volume
22
Issue
5
Start Page
1962
Last Page
1988
DOI
10.1214/11-AAP819
Abstract
We study the rate of convergence for the largest eigenvalue distributions in the Gaussian unitary and orthogonal ensembles to their Tracy–Widom limits.
We show that one can achieve an O(N−2/3) rate with particular choices of the centering and scaling constants. The arguments here also shed light on more complicated cases of Laguerre and Jacobi ensembles, in both unitary and orthogonal versions.
Numerical work shows that the suggested constants yield reasonable approximations, even for surprisingly small values of N.
Keywords
rate of convergence, random matrix, largest eigenvalue
Recommended Citation
Johnstone, I. M., & Ma, Z. (2012). Fast Approach to the Tracy–Widom Law at the Edge of GOE and GUE. The Annals of Applied Probability, 22 (5), 1962-1988. http://dx.doi.org/10.1214/11-AAP819
Date Posted: 27 November 2017
This document has been peer reviewed.