Numerical Methods for Eigenvalue Distributions of Random Matrices
Edelman, Alan ; Persson, Per-Olof
arXiv, 0501068 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-01-27
Classification:  Mathematical Physics,  Mathematics - Numerical Analysis,  15A54,  65F15 
@article{0501068,
     author = {Edelman, Alan and Persson, Per-Olof},
     title = {Numerical Methods for Eigenvalue Distributions of Random Matrices},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0501068}
}

Edelman, Alan; Persson, Per-Olof. Numerical Methods for Eigenvalue Distributions of Random Matrices. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0501068/