I'm novice to the random matrix theory (RMT), and starting out to read the Marcenko Pastur law. I noticed that there're different assumptions on the limit of ratio of number of rows to number of columns as both go to infinity. Please see below: assume that the rectangular matrix $X$, whose singular values we're intersted in, is of dimension $p\times n$, and let $p, n \to \infty.$
1) The wiki page assumes that: $\frac{p}{n}\to c$, where $c \in (0, \infty)$. Although they give different limits when $c \leq 1$ and when $c > 1$, namely, for $c > 1$, they add the term $(1 - \frac{1}{c})\mathbb{I}_{0 \in A}$. But surprisingly, the other notes/links below don't mention the cases $c > 1$ or sometimes even $c=1$. I wonder why?
2) This lecture note https://www.math.univ-toulouse.fr/~bordenave/IMPA-RMT.pdf assumes: $c \in (0,1]$. See Corollary 3.5, Page 39.
3) This note https://galton.uchicago.edu/~lalley/Courses/386/Wigner.pdf assumes $c \in (0,1)$. See Theorem 5, Page 3.
4) Terence Tao's notes on RMT: https://terrytao.files.wordpress.com/2011/02/matrix-book.pdf assumes $c \in (0,1)$. See Page 247, right before he mentions "...thanks to the Marcenko-Pastur law".
I'm not sure I'm missing something obvious here, because I don't see why the theorem being true for $c < 1$ alone would automatically prove that it's true for $c \geq 1$? I'd really appreciate some insights on this. Thank you in advance!
I'd love to have link where they state this law in full generality!