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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 595912, 7 pages
http://dx.doi.org/10.1155/2013/595912
Research Article

Second-Order Moment Convergence Rates for Spectral Statistics of Random Matrices

College of Mathematics and Information, Henan University, Kaifeng 475000, China

Received 13 June 2013; Accepted 21 October 2013

Academic Editor: Henrik Kalisch

Copyright © 2013 Junshan Xie. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper considers the precise asymptotics of the spectral statistics of random matrices. Following the ideas of Gut and Spătaru (2000) and Liu and Lin (2006) on the precise asymptotics of i.i.d. random variables in the context of the complete convergence and the second-order moment convergence, respectively, we will establish the precise second-order moment convergence rates of a type of series constructed by the spectral statistics of Wigner matrices or sample covariance matrices.