Soft modes in jammed hard spheres (I): Mean field theory of the   isostatic transition
  In this paper we consider different models for soft modes in jammed hard spheres. We show how one can construct mean field models that can be solved analytically. The analytic solution of these models displays an excess of low energy soft modes that become more and more localized by decreasing the energy. A simple solution of these models is found in the infinite dimensional limit. 
Giorgio Parisi
cond-mat.soft cond-mat.dis-nn