The divisible sandpile with heavy-tailed variables
Stochastic Processes and their Applications
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 α-stable random distribution.
Cipriani, Alessandra; Hazra, Rajat Subhra; and Ruszel, Wioletta M., "The divisible sandpile with heavy-tailed variables" (2018). Journal Articles. 1270.