Tracy-Widom law for the extreme eigenvalues of sample correlation matrices

Zhigang Bao, Guangming Pan, Wang Zhou

Let the sample correlation matrix be $W=Y{Y}^T$, where $Y=(y_{ij}{)}_{p,n}$ with $y_{ij}=x_{ij}/\sqrt{{\sum }_{j=1}^n{x}_{ij}^2}$. We assume $\{x_{ij}:1\le i\le p,1\le j\le n\}$ to be…