The Distribution of the Largest Eigenvalue in the Gaussian Ensembles

Abstract

The focus of this survey paper is on the distribution function for the largest eigenvalue in the finite N Gaussian ensembles (GOE,GUE,GSE) in the edge scaling limit of N->infinity. These limiting distribution functions are expressible in terms of a particular Painleve II function. Comparisons are made with finite N simulations as well as a discussion of the universality of these distribution functions.

13 pages

References in corpus (1)

• Universality in invariant random-matrix models: Existence near the soft edge

Cited by in corpus (10)

• Infinite N phase transitions in continuum Wilson loop operators
• From Random Matrices to Stochastic Operators
• Global spectrum fluctuations for the $\beta$-Hermite and $\beta$-Laguerre ensembles via matrix models
• On superconvergence of sums of free random variables
• Numerical Methods for Eigenvalue Distributions of Random Matrices
• Alternation of different fluctuation regimes in the stock market dynamics
• Large dimensional random k circulants
• Linear processes in high-dimension: phase space and critical properties
• Large-Dimensional Random Matrix Theory and Its Applications in Deep Learning and Wireless Communications
• Asymptotic expansions of the largest eigenvalues