Abelian sandpiles on Sierpinski gasket graphs

TL;DR

This paper studies the structure and dynamics of Abelian sandpiles on Sierpinski gasket graphs, providing a recursive description of the sandpile group and improving convergence bounds of associated Markov chains.

Contribution

It offers a new recursive characterization of the sandpile group on Sierpinski graphs and enhances understanding of the convergence speed of sandpile Markov chains.

Findings

Recursive description of the sandpile group

Characterization of the identity element

Improved bounds on Markov chain convergence

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.