## The Annals of Applied Probability

### Fast approach to the Tracy–Widom law at the edge of GOE and GUE

#### 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 $N$.

#### Article information

Source
Ann. Appl. Probab., Volume 22, Number 5 (2012), 1962-1988.

Dates
First available in Project Euclid: 12 October 2012

https://projecteuclid.org/euclid.aoap/1350067991

Digital Object Identifier
doi:10.1214/11-AAP819

Mathematical Reviews number (MathSciNet)
MR3025686

Zentralblatt MATH identifier
1253.60029

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 15B52: Random matrices

#### Citation

Johnstone, Iain M.; Ma, Zongming. Fast approach to the Tracy–Widom law at the edge of GOE and GUE. Ann. Appl. Probab. 22 (2012), no. 5, 1962--1988. doi:10.1214/11-AAP819. https://projecteuclid.org/euclid.aoap/1350067991

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