Cipriani, Alessandra ; Hazra, Rajat Subhra ; Ruszel, Wioletta M. (2018) Scaling limit of the odometer in divisible sandpiles Probability Theory and Related Fields, 172 (3-4). pp. 829-868. ISSN 0178-8051
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Official URL: http://doi.org/10.1007/s00440-017-0821-x
Related URL: http://dx.doi.org/10.1007/s00440-017-0821-x
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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Springer-Verlag. |
| Keywords: | Divisible Sandpile; Odometer; Membrane Model; Gaussian Field; Green’s Function; Abstract Wiener Space. |
| ID Code: | 121033 |
| Deposited On: | 08 Jul 2021 12:03 |
| Last Modified: | 08 Jul 2021 12:03 |
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