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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.
Original language | English |
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Pages (from-to) | 1-40 |
Number of pages | 40 |
Journal | Probability Theory and Related Fields |
Early online date | 8 Dec 2017 |
DOIs | |
Publication status | E-pub ahead of print - 8 Dec 2017 |
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Dive into the research topics of 'Scaling limit of the odometer in divisible sandpiles'. Together they form a unique fingerprint.Projects
- 1 Finished
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Early Career Fellowship - Mathematical Analysis of Strongly Correlated Processes on Discrete Dynamic Structures
Stauffer, A. (PI)
Engineering and Physical Sciences Research Council
1/04/16 → 30/09/22
Project: Research council