The critical density of the Stochastic Sandpile Model
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916655775350784 |
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| author | Campailla, Concetta Forien, Nicolas Taggi, Lorenzo |
| author_facet | Campailla, Concetta Forien, Nicolas Taggi, Lorenzo |
| contents | We study the stochastic sandpile model on $\mathbb{Z}^d$ and demonstrate that the critical density is strictly less than one in all dimensions. This generalizes a previous result by Hoffman, Hu, Richey, and Rizzolo (2022), which was limited to the one-dimensional case. In addition, we show that the critical density is strictly positive on any vertex-transitive graph, extending the earlier result of Sidoravicius and Teixeira (2018) and providing a simpler proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18905 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The critical density of the Stochastic Sandpile Model Campailla, Concetta Forien, Nicolas Taggi, Lorenzo Probability 60K35 (Primary) 82B26, 60J27 (Secondary) We study the stochastic sandpile model on $\mathbb{Z}^d$ and demonstrate that the critical density is strictly less than one in all dimensions. This generalizes a previous result by Hoffman, Hu, Richey, and Rizzolo (2022), which was limited to the one-dimensional case. In addition, we show that the critical density is strictly positive on any vertex-transitive graph, extending the earlier result of Sidoravicius and Teixeira (2018) and providing a simpler proof. |
| title | The critical density of the Stochastic Sandpile Model |
| topic | Probability 60K35 (Primary) 82B26, 60J27 (Secondary) |
| url | https://arxiv.org/abs/2410.18905 |