This article is cited in 7 papers

Short Communications

Rate of convergence to the semicircle law for the Gaussian orthogonal ensemble

D. A. Timushev^a, A. N. Tikhomirov^b, A. A. Kholopov<sup>a

a</sup> Syktyvkar State University
^b St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: It is shown that the Kolmogorov distance between the expected spectral distribution function of an $n\times n$ matrix from the Gaussian orthogonal ensemble and the distribution function of the semicircle law is of order $O(n^{-1})$.

Keywords: random matrix, semicircle law, Hermite function, Gaussian ensemble.

Received: 26.04.2006

DOI: 10.4213/tvp13

 English version: Theory of Probability and its Applications, 2008, 52:1, 171–177

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