The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 22, Number 5 (2012), 1962-1988.
Fast approach to the Tracy–Widom law at the edge of GOE and GUE
Iain M. Johnstone and Zongming Ma
Full-text: Open access
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
Permanent link to this document
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
Keywords
Rate of convergence random matrix largest eigenvalue
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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