The critical density of the Stochastic Sandpile Model

Concetta Campailla; Nicolas Forien; Lorenzo Taggi

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arXiv · 2410.18905

The critical density of the Stochastic Sandpile Model

Concetta Campailla·Nicolas Forien·Lorenzo Taggi

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Abstract

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.

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Concetta Campailla, Nicolas Forien, Lorenzo Taggi. 2024-10-24. The critical density of the Stochastic Sandpile Model. https://arxiv.org/abs/2410.18905

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