Stability at Random Close Packing
  The requirement that packings of hard particles, arguably the simplest structural glass, cannot be compressed by rearranging their network of contacts is shown to yield a new constraint on their microscopic structure. This constraint takes the form a bound between the distribution of contact forces P(f) and the pair distribution function g(r): if P(f) \sim f^{\theta} and g(r) \sim (r-{\sigma})^(-{\gamma}), where {\sigma} is the particle diameter, one finds that {\gamma} \geq 1/(2+{\theta}). This bound plays a role similar to those found in some glassy materials with long-range interactions, such as the Coulomb gap in Anderson insulators or the distribution of local fields in mean-field spin glasses. There is ground to believe that this bound is saturated, offering an explanation for the presence of avalanches of rearrangements with power-law statistics observed in packings. 
Matthieu Wyart
cond-mat.stat-mech cond-mat.dis-nn cond-mat.mtrl-sci