Edgeworth Expansion of the Largest Eigenvalue Distribution Function of GUE Revisited
Mathematical Physics
2009-11-13 v1 math.MP
Abstract
We derive expansions of the resolvent Rn(x;y;t)=(Qn(x;t)Pn(y;t)-Qn(y;t)Pn(x;t))/(x-y) of the Hermite kernel Kn at the edge of the spectrum of the finite n Gaussian Unitary Ensemble (GUEn) and the finite n expansion of Qn(x;t) and Pn(x;t). Using these large n expansions, we give another proof of the derivation of an Edgeworth type theorem for the largest eigenvalue distribution function of GUEn. We conclude with a brief discussion on the derivation of the probability distribution function of the corresponding largest eigenvalue in the Gaussian Orthogonal Ensemble (GOEn) and Gaussian Symplectic Ensembles (GSEn).
Keywords
Cite
@article{arxiv.0711.4206,
title = {Edgeworth Expansion of the Largest Eigenvalue Distribution Function of GUE Revisited},
author = {Leonard N. Choup},
journal= {arXiv preprint arXiv:0711.4206},
year = {2009}
}