  We present a generalization of the granocentric model proposed in [Clusel et
al., Nature, 2009, 460, 611615] that is capable of describing the local
fluctuations inside not only polydisperse but also monodisperse packings of
spheres. This minimal model does not take into account the relative particle
positions, yet it captures positional disorder through local stochastic
processes sampled by efficient Monte Carlo methods. The disorder is
characterized by the distributions of local parameters, such as the number of
neighbors and contacts, filled solid angle around a central particle and the
cell volumes. The model predictions are in good agreement with our experimental
data on monodisperse random close packings of PMMA particles. Moreover, the
model can be used to predict the distributions of local fluctuations in any
packing, as long as the average number of neighbors, contacts and the packing
fraction are known. These distributions give a microscopic foundation to the
statistical mechanics framework for jammed matter and allow us to calculate
thermodynamic quantities such as the compactivity in the phase space of
possible jammed configurations.
