A SHAPE THEOREM FOR EXPLODING SANDPILES

• 成果类型: Article
• 署名作者: Bou-Rabee, Ahmed
• 署名单位: University of Chicago
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1976
• 发表日期: 2024
• 页码: 714-742
• 关键词: stochastic homogenization; chemical distance; abelian sandpile; laplacian growth; limiting shapes; DYNAMICS; CONVERGENCE; percolation

摘要

We study scaling limits of exploding Abelian sandpiles using ideas from percolation and front propagation in random media. We establish sufficient conditions under which a limit shape exists and show via a family of counter-examples that convergence may not occur in general. A corollary of our proof is a simple criterion for determining if a sandpile is explosive; this strengthens a result of Fey, Levine and Peres (J. Stat. Phys. (2010) 138 143-159).