Distribution of the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy-Widom distribution

Abstract

We derive efficient recursive formulas giving the exact distribution of the largest eigenvalue for finite dimensional real Wishart matrices and for the Gaussian Orthogonal Ensemble (GOE). In comparing the exact distribution with the limiting distribution of large random matrices, we also found that the Tracy-Widom law can be approximated by a properly scaled and shifted Gamma distribution, with great accuracy for the values of common interest in statistical applications.

Journal of Multivariate Analysis (2014)

References in corpus (4)

• Exact scaling functions for one-dimensional stationary KPZ growth
• High Dimensional Statistical Inference and Random Matrices
• Accuracy of the Tracy--Widom limits for the extreme eigenvalues in white Wishart matrices
• Fast approach to the Tracy-Widom law at the edge of GOE and GUE

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