Scaling limit of the odometer in divisible sandpiles

Authors

Alessandra Cipriani, University of Bath
Rajat Subhra Hazra, Indian Statistical Institute, Kolkata
Wioletta M. Ruszel, Delft University of Technology

Article Type

Research Article

Publication Title

Probability Theory and Related Fields

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.

First Page

829

Last Page

868

DOI

10.1007/s00440-017-0821-x

Publication Date

12-1-2018

Comments

All Open Access, Hybrid Gold, Green

Recommended Citation

Cipriani, Alessandra; Hazra, Rajat Subhra; and Ruszel, Wioletta M., "Scaling limit of the odometer in divisible sandpiles" (2018). Journal Articles. 1153.
https://digitalcommons.isical.ac.in/journal-articles/1153