The Abelian Sandpile: a Mathematical Introduction

R. Meester, F. Redig, D. Znamenski

2001, v.7, №4, 509-523


We give a simple rigorous 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.

Keywords: abelian sandpile,recurrent configurations,burning algorithm


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