Scaling limit of the odometer in divisible sandpiles
Alessandra Cipriani (University of Bath)
Rajat Subhra Hazra (Indian Statistical Institute)
Wioletta Ruszel (TU Delft - Applied Probability)
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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.
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