  We show that random matrix models are a natural tool for understanding the
appearance of a large gap in the microstate spectrum of black holes when there
is a high degeneracy of states, in a variety of settings. While the most
natural context is extended supersymmetry, where the number of BPS states
scales as ${\rm e}^{S_0}$, where $S_0$ is the $T{=}0$ entropy, it is a robust
feature that a large gap will appear whenever there is a mechanism producing a
high degree of degeneracy. In random matrix model terms, the phenomenon is
simply an extreme case of eigenvalue repulsion in the effective log gas
description. We exhibit several examples for illustration, starting with the
simple Wishart model, continuing with extensions of it that incorporate
multicritical behaviour allowing for the emergence of gravity, and culminating
in using such models to non-perturbatively construct ${N}{=}2$ and ${N}{=}4$ JT
supergravity theories, the latter of which is new.
