The critical density of the Stochastic Sandpile Model

2024/10/24 by Concetta Campailla, Campailla, Concetta, Nicolas Forien +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #60J27 (Secondary) #60K35 (Primary) 82B26 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2410.18905

openalex publication_date 2024/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the stochastic sandpile model on 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.

Cited by

• Stochastic Sandpile model: exact sampling and complete graph

Related

• Active Phase for the Stochastic Sandpile on Z
• Critical densities in sandpile models with quenched or annealed disorder
• Stochastic Sandpile model: exact sampling and complete graph
• Restricted sandpile revisited
• The divisible sandpile with heavy-tailed variables