  We estimate numerically the normal modes of the free energy in a glass of
hard discs. We observe that, near the glass transition or after a rapid quench
deep in the glass phase, the density of states (i) is characteristic of a
marginally stable structure, in particular it di splays a frequency scale
$\omega^*\sim p^{1/2}$, where $p$ is the pressure and (ii) gives a faithful
representation of the short-time dyn amics. This brings further evidences that
the boson peak near the glass transition corresponds to the relaxation of
marginal modes of a we akly-coordinated structure, and implies that the mean
square displacement in the glass phase is anomalously large and goes as $<
\delta R^2 > \sim p^{-3/2}$, a prediction that we check numerically.
