Finite n Largest Eigenvalue Probability Distribution Function of Gaussian Ensembles

Details Finite n Largest Eigenvalue Probability Distribution Function of Gaussian Ensembles Finite n Largest Eigenvalue Probability Distribution Function of Gaussian Ensembles

2011-01-27

arxiv.org/abs/1101.5219v1

Mathematics

Probability

15 pages

Scientific paper

In this paper we focus on the finite n probability distribution function of the largest eigenvalue in the classical Gaussian Ensemble of n by n matrices (GEn). We derive the finite n largest eigenvalue probability distribution function for the Gaussian Orthogonal and Symplectic Ensembles and also prove an Edgeworth type Theorem for the largest eigenvalue probability distribution function of Gaussian Symplectic Ensemble. The correction terms to the limiting probability distribution are expressed in terms of the same Painleve II functions appearing in the Tracy-Widom distribution.

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