Second-order moment convergence rates for spectral statistics of random matrices. (English) Zbl 1432.60016

Summary: This paper considers the precise asymptotics of the spectral statistics of random matrices. Following the ideas of A. Gut and A. Spătaru [J. Math. Anal. Appl. 248, No. 1, 233–246 (2000; Zbl 0961.60039); Ann. Probab. 28, No. 4, 1870–1883 (2000; Zbl 1044.60024)] and W. Liu and Z. Lin [Stat. Probab. Lett. 76, No. 16, 1787–1799 (2006; Zbl 1104.60015)] 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.


60B20 Random matrices (probabilistic aspects)
15B52 Random matrices (algebraic aspects)
60F15 Strong limit theorems
Full Text: DOI


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