  To better understand the surprising low-frequency vibrational modes in
structural glasses, we study the spectra of a large ensemble of sparse random
matrices where disorder is controlled by the distribution of bond weights and
network coordination. We find $D(\omega)$ has three regimes: a
very-low-frequency regime that can be predicted analytically using extremal
statistics, an intermediate regime with quasi-localized modes, and a plateau
with $D(\omega) \sim \omega^0$. In the special case of uniform bond weights,
the intermediate regime displays $D(\omega) \sim \omega^4$, independent of
network coordination and system size, just as recently discovered in
simulations of structural glasses.
