Scaling limit of the odometer in divisible sandpiles

In a recent work Levine et al. (Ann Henri Poincaré 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 t...

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Autores principales: Cipriani, Alessandra, Hazra, Rajat Subhra, Ruszel, Wioletta M.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2017
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6405076/
https://www.ncbi.nlm.nih.gov/pubmed/30930516
http://dx.doi.org/10.1007/s00440-017-0821-x
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author Cipriani, Alessandra
Hazra, Rajat Subhra
Ruszel, Wioletta M.
author_facet Cipriani, Alessandra
Hazra, Rajat Subhra
Ruszel, Wioletta M.
author_sort Cipriani, Alessandra
collection PubMed
description In a recent work Levine et al. (Ann Henri Poincaré 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.
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spelling pubmed-64050762019-03-27 Scaling limit of the odometer in divisible sandpiles Cipriani, Alessandra Hazra, Rajat Subhra Ruszel, Wioletta M. Probab Theory Relat Fields Article In a recent work Levine et al. (Ann Henri Poincaré 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. Springer Berlin Heidelberg 2017-12-08 2018 /pmc/articles/PMC6405076/ /pubmed/30930516 http://dx.doi.org/10.1007/s00440-017-0821-x Text en © The Author(s) 2017 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Cipriani, Alessandra
Hazra, Rajat Subhra
Ruszel, Wioletta M.
Scaling limit of the odometer in divisible sandpiles
title Scaling limit of the odometer in divisible sandpiles
title_full Scaling limit of the odometer in divisible sandpiles
title_fullStr Scaling limit of the odometer in divisible sandpiles
title_full_unstemmed Scaling limit of the odometer in divisible sandpiles
title_short Scaling limit of the odometer in divisible sandpiles
title_sort scaling limit of the odometer in divisible sandpiles
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6405076/
https://www.ncbi.nlm.nih.gov/pubmed/30930516
http://dx.doi.org/10.1007/s00440-017-0821-x
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