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?

Thank you for your answer!