This article is cited in 2 papers

Short Communications

The rate of convergence in probability for spectra of the GUE

D. A. Timushev

Syktyvkar State University

Abstract: 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 $O_p((\log n)/n^{2/3})$.

Keywords: random matrix, semicircle law, Wigner ensemble, Gaussian unitary ensemble.

Received: 13.06.2006

DOI: 10.4213/tvp45

 English version: Theory of Probability and its Applications, 2007, 51:3, 546–549

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