Dynamic dimensional reduction in the Abelian sandpile
Probability
2022-07-29 v2 Analysis of PDEs
Combinatorics
Abstract
We prove the dimensional reduction conjecture of Fey, Levine, and Peres (2010) on the hypercube. The proof shows that dimensional reduction, symmetry, and regularity of the Abelian sandpile persist during the parallel toppling process. This stronger result verifies empirical observations first documented by Liu, Kaplan, and Gray (1990).
Cite
@article{arxiv.2009.05968,
title = {Dynamic dimensional reduction in the Abelian sandpile},
author = {Ahmed Bou-Rabee},
journal= {arXiv preprint arXiv:2009.05968},
year = {2022}
}
Comments
25 pages, 4 figures, 1 table; expanded exposition and some minor corrections