Scaling limit of the odometer in divisible sandpiles
| Autor: | Rajat Subhra Hazra, Alessandra Cipriani, Alexandre Stauffer, Wioletta Ruszel |
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| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
Pure mathematics Divisible sandpile Mathematics::Dynamical Systems odometer 82C20 Dimension (graph theory) bilaplacian kernel gaussian field Field (mathematics) Green’s function 31B30 01 natural sciences Odometer Article membrane model 010104 statistics & probability 60J45 FOS: Mathematics scaling limit 0101 mathematics Mathematics Gaussian field Continuum (topology) Abelian sandpile model Abstract Wiener space 010102 general mathematics Probability (math.PR) Torus Function (mathematics) Green's function bilaplacian Gaussian field Scaling limit Membrane model 60G15 Statistics Probability and Uncertainty divisible sandpile Analysis Mathematics - Probability |
| Zdroj: | Probability Theory and Related Fields Probability Theory and Related Fields, 172(3-4) Probability Theory and Related Fields, 172(3-4), 829. Springer New York |
| ISSN: | 0178-8051 |
| DOI: | 10.48550/arxiv.1604.03754 |
| Popis: | In a recent work Levine et al. (2015) 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. Comment: 29 pages. Minor corrections in the proof of the scaling limit for general weights made |
| Databáze: | OpenAIRE |
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