Precise asymptotics on spectral statistics of random matrices

Abstract

This paper focuses on the limiting properties of the spectral statistics of Wigner matrices and sample covariance matrices. Following the ideas of Gut and Spaˇtaru (2000a, b), Gut and Steinebach (2013) and Chow (1988) on precise asymptotics of i.i.d. random variables in the context of complete convergence and moment convergence, we will establish the corresponding results on the spectral statistics of random matrices.