Scaling limit of the odometer in divisible sandpiles

Alessandra Cipriani, Rajat Subhra Hazra, Wioletta Magdalena Ruszel

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

In a recent work Levine et al. (Ann Henri Poincaré 17:1677–1711, 2016. https://doi.org/10.1007/s00023-015-0433-x) 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)1-40
Number of pages40
JournalProbability Theory and Related Fields
Early online date8 Dec 2017
DOIs
Publication statusE-pub ahead of print - 8 Dec 2017

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