Differential Equations for Laguerre Orthogonal Ensemble

Dr. Leonard Choup

Department of Mathematical Sciences
UAHuntsville

12 November 2010
218 Shelby Center
3:00 (Refreshements at 2:30)

Abstract

We derive a representation of the probability distribution function of the largest eigenvalue from the Laguerre Orthogonal Ensemble of Random Matrix Theory. We show that the corresponding representation satisfies a system of differential equations, whose solution can be expressed in terms of the Hastings-McLeod solution of Painlevé equation. Finally, we show that this solution can be used to give a large N expansion of the desired largest eigenvalue distribution function.