The Abelian sandpile; a mathematical introduction

Abstract

We give a simple rigourous treatment of the classical results of the abelian sandpile model. Although we treat results which are well-known in the physics literature, in many cases we did not find complete proofs in the literature. The paper tries to fill the gap between the mathematics and the physics literature on this subject, and also presents some new proofs. It can also serve as an introduction to the model.

19 pages

References in corpus (1)

• Studying Self-Organized Criticality with Exactly Solved Models

Cited by in corpus (9)

• On the Sandpile group of the cone of a graph
• Infinite volume limit of the Abelian sandpile model in dimensions d >= 3
• Limiting shapes for deterministic centrally seeded growth models
• A family of bijections between G-parking functions and spanning trees
• Limiting shapes for a non-abelian sandpile growth model and related cellular automata
• Avalanche dynamics of the Abelian sandpile model on the expanded cactus graph
• The Abelian Sandpile Model on Fractal Graphs
• Existence and uniqueness of the stationary measure in the continuous Abelian sandpile
• Critical densities in sandpile models with quenched or annealed disorder