Unbounded Largest Eigenvalue of Large Sample Covariance Matrices: Asymptotics, Fluctuations and Applications

Florence Merlevède, Jamal Najim, Peng Tian

Given a large sample covariance matrix $S_N=\frac{1}{n}{\Gamma }_N^{1/2}{Z}_N{Z}_N^{\ast }{\Gamma }_N^{1/2},$ where $Z_N$ is a $N\times n$ matrix with i.i.d. centered entries, and ${\Gamma }_N$ is a $N\times N$ de…