On Painleve Related Functions Arising in Random Matrix Theory

2011/01/27 by Choup, Leonard N.
#60B20 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1101.5218

Abstract

In deriving large n probability distribution function of the rightmost eigenvalue from the classical Random Matrix Theory Ensembles, one is faced with que question of finding large n asymptotic of certain coupled set of functions. This paper presents some of these functions in a new light.

Related

• Distribution functions for largest eigenvalues and their applications
• Painleve formulas of the limiting distributions for non-null complex sample covariance matrices
• Asymptotic properties of a family of solutions of the Painleve equation PVI
• Universality of the distribution functions of random matrix theory
• Airy Kernel and Painleve II