I am reading about the Marchenko-Pastur Law (https://people.math.wisc.edu/~valko/courses/833/2009f/lec_6_7.pdf) and trying to decipher the main theorem so it is more intituitive.
Would it mean in any case that if $p/n \rightarrow 1$ (or $y$ is close to 1), then the singular values of a matrix $X$ (or the eigenvalues of $XX'$) are more likely to include one that is close to 0?