Exact solution of stochastic directed sandpile model
  We introduce and analytically solve a directed sandpile model with stochastic toppling rules. The model clearly belongs to a different universality class from its counterpart with deterministic toppling rules, previously solved by Dhar and Ramaswamy. The critical exponents are D_||=7/4, \tau=10/7 in two dimensions and D_||=3/2, \tau=4/3 in one dimension. The upper critical dimension of the model is three, at which the exponents apart from logarithmic corrections reach their mean-field values D_||=2, \tau=3/2. 
Morten Kloster, Sergei Maslov, Chao Tang