A shape theorem for exploding sandpiles
Probability
2023-05-03 v2 Analysis of PDEs
Combinatorics
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 criteria for determining if a sandpile is explosive; this strengthens a result of Fey, Levine, and Peres (2010).
Cite
@article{arxiv.2102.04422,
title = {A shape theorem for exploding sandpiles},
author = {Ahmed Bou-Rabee},
journal= {arXiv preprint arXiv:2102.04422},
year = {2023}
}
Comments
31 pages, 5 figures, 1 table; some minor revisions