  We track the motion of a horizontally vibrated amorphous assembly of
bidisperse hard disks, for densities ranging across the jamming transition. We
derive on very general grounds a bound on the dynamical susceptibility in terms
of the response of the dynamics to a change in density. This generalizes a
similar bound recently derived for equilibrium liquids. We find that in our
experimental system the bound is tight and reproduces the non-monotonic
behavior of the dynamical susceptibility both in time and density across the
jamming transition. The underlying scaling behavior reveals an intimate
connection between anomalous diffusion and dynamical heterogeneity.
