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- ItemThe divisible sandpile with heavy-tailed variables(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Cipriani, Alessandra; Hazra, Rajat Subhra; Ruszel, Wioletta M.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.
- ItemScaling limit of the odometer in divisible sandpiles(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Cipriani, Alessandra; Hazra, Rajat Subra; Ruszel, Wioletta M.In a recent work Levine et al. (2015) prove that the odometer function of a divisible sandpile model on a finite graph can be expressed as a shifted discrete bilaplacian Gaussian field. For the discrete torus, they suggest the possibility that the scaling limit of the odometer may be related to the continuum bilaplacian field. In this work we show that in any dimension the rescaled odometer converges to the continuum bilaplacian field on the unit torus