Fast Approach to the Tracy-widom Law at the Edge of Goe and Gue.
نویسندگان
چکیده
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 suprisingly small values of N.
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عنوان ژورنال:
- The annals of applied probability : an official journal of the Institute of Mathematical Statistics
دوره 22 5 شماره
صفحات -
تاریخ انتشار 2012