Geodesic
The rate of convergence in probability for spectra of the GUE
Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 3, pp. 618-622

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It is shown that the Kolmogorov distance between the spectral distribution function of an $n\times n$ matrix from the Gaussian unitary ensemble (GUE) and the distribution function of the semicircle law is of stochastic order $O_p((\log n)/n^{2/3})$.
Mots-clés : random matrix, Wigner ensemble
Keywords: semicircle law, Gaussian unitary ensemble. 
@article{TVP_2006_51_3_a12,
     author = {D. A. Timushev},
     title = {The rate of convergence in probability for spectra of the {GUE}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {618--622},
     publisher = {mathdoc},
     volume = {51},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2006_51_3_a12/}
}
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D. A. Timushev. The rate of convergence in probability for spectra of the GUE. Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 3, pp. 618-622. http://geodesic.mathdoc.fr/item/TVP_2006_51_3_a12/