# Marcenko-Pastur and Tracy-Widom laws for sample covariance and Gram matrices when the "features" are correlated: references

Let us assume we've a rectangular data matrix $$X=[x_1 \dots x_n] \in \mathbb{R}^{p \times n}$$, where the $$x_i \in \mathbb{R}^{p \times 1}$$ are iid column vectors. I'm not assuming here that the entries of the matrix $$X$$ are iid, or also that $$x_i$$ are of the form $$x_i = C^{1/2}z_i$$, where $$Z:=[z_1 \dots z_n]$$ have iid entries (I think the work of Baik and Silverstein includes this case for ESD's). I'm really assuling that the co-ordinates ("features") of each $$x_i$$ are corelated.

I'm wondering (some references will be enough, but detailed answers appreciated!) if there're equivalents of Marcenko-Pastur and Tracy-Wisdom theorems in this case? More precisely:

(1) What's the limiting empirical spectral distribution of sample covariance $$\frac{1}{p}XX'$$ and Gram matrix $$\frac{1}{n}X'X$$?

(2) How are the largest eigenvalues of the above two matrices distributed?