Abstract
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 counterexamples 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).
Acknowledgments
Thank you to Charles K. Smart for motivating, helpful discussions during this project. Thank you to Lionel Levine for several inspiring conversations and for suggesting this question. Thank you to Dylan Airey for asking if exploding sandpiles have a limit shape.
Citation
Ahmed Bou-Rabee. "A shape theorem for exploding sandpiles." Ann. Appl. Probab. 34 (1A) 714 - 742, February 2024. https://doi.org/10.1214/23-AAP1976
Information
