On Concentration of Empirical Measures and Convergence to the Semi-circle Law

Author: Bobkov S.  

Publisher: Springer Publishing Company

ISSN: 0894-9840

Source: Journal of Theoretical Probability, Vol.23, Iss.3, 2010-09, pp. : 792-823

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Abstract

Concentration properties of the general empirical distribution functions and the rate of convergence of spectral empirical distributions to the semi-circle law in the case of symmetric high-dimensional random matrices are studied under Poincaré-type inequalities.