  We consider zero temperature packings of soft spheres, that undergo a jamming
to unjamming transition as a function of packing fraction. We compare
differences in the structure, as measured from the contact statistics, of a
finite subsystem of a large packing to a whole packing with periodic boundaries
of an equivalent size and pressure. We find that the fluctuations of the
ensemble of whole packings are smaller than those of the ensemble of
subsystems. Convergence of these two quantities appears to occur at very large
systems, which are usually not attainable in numerical simulations. Finding
differences between packings in two dimensions and three dimensions, we also
consider four dimensions and mean-field models, and find that they show similar
system size dependence. Mean-field critical exponents appear to be consistent
with the 3d and 4d packings, suggesting they are above the upper critical
dimension. We also find that the convergence as a function of system size to
the thermodynamic limit is characterized by two different length scales. We
argue that this is the result of the system being above the upper critical
dimension.
