Universality in the bulk of the spectrum for complex sample covariance matrices

Details Universality in the bulk of the spectrum for complex sample covariance matrices Universality in the bulk of the spectrum for complex sample covariance matrices

2009-12-13

arxiv.org/abs/0912.2493v2

Mathematics

Probability

Typos corrected, figures and exposition improved

Scientific paper

We consider complex sample covariance matrices $M_N=\frac{1}{N}YY^*$ where $Y$ is a $N \times p$ random matrix with i.i.d. entries $Y_{ij}, 1\leq i\leq N, 1\leq j \leq p$ with distribution $F$. Under some regularity and decay assumption on $F$, we prove universality of some local eigenvalue statistics in the bulk of the spectrum in the limit where $N\to \infty$ and $\lim_{N \to \infty}p/N =\gamma$ for any real number $\gamma \in (0, \infty)$.

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