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We track the motion of a horizontally vibrated amorphous assembly ofbidisperse hard disks, for densities ranging across the jamming transition. Wederive on very general grounds a bound on the dynamical susceptibility in termsof the response of the dynamics to a change in density. This generalizes asimilar bound recently derived for equilibrium liquids. We find that in ourexperimental system the bound is tight and reproduces the non-monotonicbehavior of the dynamical susceptibility both in time and density across thejamming transition. The underlying scaling behavior reveals an intimateconnection between anomalous diffusion and dynamical heterogeneity.

Lower bound on the four-point dynamical susceptibility: Direct experimental test on a granular packing