I will refer to the following publicly available source to keep the discussion contained:
https://zhenyu-liao.github.io/pdf/RMT4ML.pdf
In Equation (2.10) they specify the Marcenko Pastur distribution, with a Dirac Delta which activates for the case of $c > 1$ (N.B. the activation is due to the definition of $(x)^+ = \max(0,x)$:
After here (on page 61), the authors discuss that there is a clustering of eigenvalues that occur for the setting $c > 1$, and that when $c = 1$ there is a phenomenon for the distribution to approach $\infty$ as $c\rightarrow 0$. Furthermore, there is an interesting elongation in the shape of the density function for $c>1$.
I was wondering if there are any sources which discuss this phenomenon in much more detail, as well as any implications it might have?
The authors of this book claim its importance for a particular phenomenon in machine learning (called double descent), but after that I can't locate where in the book they discuss this in any more detail.... To be fair in the subsection:
Model complexity and the double descent phenomenon
They try to push for more detail, but in my opinion it feels somewhat lacking in reference to the behavior of the Marcenko Pastur distribution. Rather it is a discussion centered upon the invertibility of matrices, and a technical angle of taking limits. It is a justification of sorts, but it does feel like it is lacking a deeper, intuitive understanding, and the problem is "brushed away" too easily like it is therefore solved.
For some people, this analytic approach is sufficient, but for myself I would like to see more discussion on this phenomenon, especially as it relates to the Marcenko Pastur distribution. Therefore I am wondering if anyone has any further references / texts that go in more detail around this $c\geq 1$ transition that is observed in the Marcenko Pastur distribution?
I am hoping that approaching this phenomenon from a variety of different angles will help me a lot.
Thanks!