The divisible sandpile with heavy-tailed variables
  This work deals with the divisible sandpile model when an initial configuration sampled from a heavy-tailed distribution. Extending results of Levine et al. (2015) and Cipriani et al. (2016) we determine sufficient conditions for stabilization and non-stabilization on infinite graphs. We determine furthermore that the scaling limit of the odometer on the torus is an $\alpha$-stable random distribution. 
Alessandra Cipriani, Rajat Subhra Hazra, Wioletta M. Ruszel
math.PR