The divisible sandpile with heavy-tailed variables
- Cipriani, Alessandra
- Hazra, Rajat Subra
- Ruszel, Wioletta M.
2010 Mathematics Subject Classification
- 60G52 60J45 60G15 82C20
- divisible sandpile, heavy-tailed variables, alpha-stable random distribution
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.
- Stochastic Processes and their Applications, 128 (2018), pp. 3054--3081.