On the structure of the sandpile identity element on Sierpinski gasket graphs
Combinatorics
2026-03-13 v1 Probability
Abstract
We consider the identity of the abelian sandpile group of finite approximation graphs of the Sierpinski gasket, and we show that the second-order term in the scaling limit converges to the path distance to the nearest corner on the Sierpinski gasket. The proof relies on a decomposition of the identity of the sandpile group into the sum of a constant function and the Laplacian of the graph distance on the approximating graphs.
Keywords
Cite
@article{arxiv.2603.12006,
title = {On the structure of the sandpile identity element on Sierpinski gasket graphs},
author = {Robin Kaiser and Ecaterina Sava-Huss and Julia Überbacher},
journal= {arXiv preprint arXiv:2603.12006},
year = {2026}
}
Comments
14 pages, 11 figures