Rigorous stochastic bounds for the error in large covariance matrices

This paper is motivated by recent studies of Huang et al. on distributed PCA and network anomaly detection and contains a rigorous derivation of bounds for the expected value and the variance of the spectral norm of the error in large covariance matrices. This derivation is based on a deep result by Yin et al. (Probab. Theor. Relat. Fields 1988; 78:509-521), which gives the asymptotics of the maximal eigenvalue of a random matrix as the matrix dimension goes to infinity.