This article is cited in 9 papers

Short Communications

Rate of convergence to the semi-circular law for the Gaussian unitary ensemble

F. Götze^a, A. N. Tikhomirov<sup>b

a</sup> Bielefeld University, Department of Mathematics
^b Syktyvkar State University

Abstract: It is shown that the Kolmogorov distance between the expected spectral distribution function of an $n\times n$ Wigner matrix with Gaussian elements and the distribution function of the semicircular law is of order $O(n^{-2/3})$.

Keywords: independent random variables, spectral distribution, random matrix.

Received: 08.02.2002

Language: English

DOI: 10.4213/tvp3670

 English version: Theory of Probability and its Applications, 2003, 47:2, 323–330

Bibliographic databases:

• 
• 
•