ScholarlyCommons

Title

Fast Approach to the Tracy–Widom Law at the Edge of GOE and GUE

Author(s)

Iain M. Johnstone
Zongming Ma, University of Pennsylvania

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