I have some trouble to understand the difference between the "bulk" and the "edges" of the spectral density of random matrices (for instance in this question).
From my understanding, all properties of random matrices eigenvalues are actually only valid in the bulk (correlations for instance). But where does the separation begin ?
Let's take the example of Gaussian matrices. For instance, for 8x8 or 100x100 random matrices from the GOE, the spectral density looks like:
I initially thought "the bulk" designated for these matrices the inner part of the Wigner semi-circle, while the edges were the outer parts. Is such a crude guess a valid approximation (for practical applications for instance) ?