Force distributions in a triangular lattice of rigid bars
  We study the uniformly weighted ensemble of force balanced configurations on a triangular network of nontensile contact forces. For periodic boundary conditions corresponding to isotropic compressive stress, we find that the probability distribution for single-contact forces decays faster than exponentially. This super-exponential decay persists in lattices diluted to the rigidity percolation threshold. On the other hand, for anisotropic imposed stresses, a broader tail emerges in the force distribution, becoming a pure exponential in the limit of infinite lattice size and infinitely strong anisotropy. 
Brian P. Tighe, Joshua E. S. Socolar, David G. Schaeffer, W. Garrett   Mitchener, and Mark L. Huber