Scaling limit of the odometer in divisible sandpiles

• 成果类型: Article
• 署名作者: Cipriani, Alessandra; Hazra, Rajat Subhra; Ruszel, Wioletta M.
• 署名单位: University of Bath; Indian Statistical Institute; Indian Statistical Institute Kolkata; Delft University of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0821-x
• 发表日期: 2018
• 页码: 829-868
• 关键词: entropic repulsion; models

摘要

In a recent work Levine et al. (Ann Henri Poincare 17:1677-1711, 2016. 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.