Convergence of the largest eigenvalue of normalized sample covariance matrices when p and n both tend to infinity with their ratio converging to zero

B. B. Chen, G. M. Pan

Let ${\mathbf{X}}_p=({\mathbf{s}}_1,...,{\mathbf{s}}_n)=(X_{ij}{)}_{p\times n}$ where $X_{ij}$'s are independent and identically distributed (i.i.d.) random variables with $EX_{11}=0,EX_{…