Abelian sandpiles on Sierpinski gasket graphs

2022/09/07 by Robin Kaiser, Kaiser, Robin, Ecaterina Sava‐Huss +3
Computer Science · Mathematics · #05C81 #20K01 #31C20 #60J10 #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Probability (math.PR) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2209.03169

openalex publication_date 2022/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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