Scaling limit of the odometer in divisible sandpiles
Probability
2017-11-29 v4
Abstract
In a recent work Levine et al. (2015) 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.
Keywords
Cite
@article{arxiv.1604.03754,
title = {Scaling limit of the odometer in divisible sandpiles},
author = {Alessandra Cipriani and Rajat Subhra Hazra and Wioletta M. Ruszel},
journal= {arXiv preprint arXiv:1604.03754},
year = {2017}
}
Comments
29 pages. Minor corrections in the proof of the scaling limit for general weights made