Scaling limit of the odometer in divisible sandpiles

Journal article (2018)

Authors

A. Cipriani University of Bath
Rajat Subhra Hazra Indian Statistical Institute
W.M. Ruszel Applied Probability - EEMCS
Research Group
Applied Probability (EEMCS) (TU Delft)
Copyright: © 2018 A. Cipriani, Rajat Subhra Hazra, W.M. Ruszel
DOI: https://doi.org/10.1007/s00440-017-0821-x
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Published Date

2018

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

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.