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arXiv · 0711.4206

Edgeworth Expansion of the Largest Eigenvalue Distribution Function of GUE Revisited

Leonard N. Choup
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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).

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Leonard N. Choup. 2007-11-27. Edgeworth Expansion of the Largest Eigenvalue Distribution Function of GUE Revisited. https://doi.org/10.1063/1.2873345

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