WIAS Preprint No. 2328, (2016)

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.

Appeared in

  • Stochastic Processes and their Applications, 128 (2018), pp. 3054--3081.

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