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Numerical Methods for Eigenvalue Distributions of Random Matrices

Alan Edelman·Per-Olof Persson
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Abstract

We present efficient numerical techniques for calculation of eigenvalue distributions of random matrices in the beta-ensembles. We compute histograms using direct simulations on very large matrices, by using tridiagonal matrices with appropriate simplifications. The distributions are also obtained by numerical solution of the Painleve II and V equations with high accuracy. For the spacings we show a technique based on the Prolate matrix and Richardson extrapolation, and we compare the distributions with the zeros of the Riemann zeta function.

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Alan Edelman, Per-Olof Persson. 2005-01-27. Numerical Methods for Eigenvalue Distributions of Random Matrices. https://arxiv.org/abs/math-ph/0501068

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