We obtain optimal bounds of order O(n −1) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution functions of random matrices from the GUE and LUE, respectively.
@article{bwmeta1.element.doi-10_2478_BF02475626,
author = {Friedrich G\"otze and Alexander Tikhomirov},
title = {The rate of convergence for spectra of GUE and LUE matrix ensembles},
journal = {Open Mathematics},
volume = {3},
year = {2005},
pages = {666-704},
zbl = {1108.60014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475626}
}
Friedrich Götze; Alexander Tikhomirov. The rate of convergence for spectra of GUE and LUE matrix ensembles. Open Mathematics, Tome 3 (2005) pp. 666-704. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475626/
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