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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 decayassumption on $F$, we prove universality of some local eigenvalue statistics inthe bulk of the spectrum in the limit where $N\to \infty$ and $\lim_{N \to\infty}p/N =\gamma$ for any real number $\gamma \in (0, \infty)$.

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