Date of this Version
The Annals of Applied Probability
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.
rate of convergence, random matrix, largest eigenvalue
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.