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

Xie, Junshan

Abstr. Appl. Anal. 2013, Article ID 595912, 7 p. (2013).

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.

MSC:

60B20	Random matrices (probabilistic aspects)
15B52	Random matrices (algebraic aspects)
60F15	Strong limit theorems

Keywords:

precise asymptotics; spectral statistics of random matrices

Citations:

Zbl 0961.60039; Zbl 1044.60024; Zbl 1104.60015

References:

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