Hao-Zhu Zhao

Phase transition for the smallest eigenvalue of high-dimensional sample correlation matrices

We study the smallest nonzero eigenvalue of the sample correlation matrix $\mathbf{R}_n$ formed from a $p_n \times n$ data matrix with i.i.d. real entries $\xi$ of mean zero and unit variance, in the high-dimensional regime $p_n / n \to \phi \in (0, \infty) \setminus \{1\}$. In the tall regime $\phi>1$, we prove almost...