Scaling limit of the odometer in divisible sandpiles

Alessandra Cipriani, Rajat Subhra Hazra, Wioletta Ruszel

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)
33 Downloads (Pure)


In a recent work Levine et al. (Ann Henri Poincaré 17:1677–1711, 2016. 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.

Original languageEnglish
Pages (from-to)829-868
Number of pages40
JournalProbability Theory and Related Fields
Issue number3-4
Publication statusPublished - 2018


  • Divisible sandpile
  • Odometer
  • Membrane model
  • Gaussian field
  • Green’s function
  • Abstract Wiener space


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