On Painleve Related Functions Arising in Random Matrix Theory

TL;DR

This paper explores Painleve-related functions that emerge in the asymptotic analysis of the largest eigenvalue distribution in classical random matrix ensembles, offering new insights into their properties.

Contribution

It introduces a novel perspective on Painleve-related functions associated with large n asymptotics in random matrix theory.

Findings

New characterization of Painleve-related functions in random matrix theory

Enhanced understanding of asymptotic behavior of eigenvalue distributions

Potential applications to statistical physics and complex systems

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.