2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167570We 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.5 pages, 3 figuresSoft Condensed Mattertext