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arXiv · 2209.03169

Abelian sandpiles on Sierpinski gasket graphs

Robin Kaiser·Ecaterina Sava-Huss·Yuwen Wang
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Abstract

The aim of the current work is to investigate structural properties of the sandpile group of a special class of self-similar graphs. More precisely, we consider Abelian sandpiles on Sierpinski gasket graphs and for the choice of normal boundary conditions, we give a characterization of the identity element and a recursive description of the sandpile group. Finally, we consider Abelian sandpile Markov chains on the aforementioned graphs and we improve the existing bounds on the speed of convergence to stationarity.

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Robin Kaiser, Ecaterina Sava-Huss, Yuwen Wang. 2022-09-07. Abelian sandpiles on Sierpinski gasket graphs. https://arxiv.org/abs/2209.03169

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