WIAS Preprint No. 2268, (2016)

Scaling limit of the odometer in divisible sandpiles


  • Cipriani, Alessandra
  • Hazra, Rajat Subra
  • Ruszel, Wioletta M.


  • divisible sandpile, bilaplacian Gaussian field, bilaplacian kernel, scaling limit




In a recent work [LMPU] 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.

Appeared in

  • Probab. Theory Related Fields, 172 (2018), pp. 829-868.

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