Guang-Chen Chen

Tracy-Widom law for sample covariance matrices under quadratic form concentration

We study sample covariance matrices formed from vectors $q_i = \Sigma^{1/2}u_i \in \mathbb{R}^M$, $1 \leq i \leq N$, where $u_1, \ldots, u_N$ are independent, centered, isotropic random vectors whose coordinates may not be independent. We assume that the random vectors $q_i$ satisfy a concentration bound for their quad...