Open Access
2018 Sandpile models
Antal A. Járai
Probab. Surveys 15: 243-306 (2018). DOI: 10.1214/14-PS228


This survey is an extended version of lectures given at the Cornell Probability Summer School 2013. The fundamental facts about the Abelian sandpile model on a finite graph and its connections to related models are presented. We discuss exactly computable results via Majumdar and Dhar’s method. The main ideas of Priezzhev’s computation of the height probabilities in 2D are also presented, including explicit error estimates involved in passing to the limit of the infinite lattice. We also discuss various questions arising on infinite graphs, such as convergence to a sandpile measure, and stabilizability of infinite configurations.


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Antal A. Járai. "Sandpile models." Probab. Surveys 15 243 - 306, 2018.


Received: 1 January 2014; Published: 2018
First available in Project Euclid: 24 September 2018

zbMATH: 06942909
MathSciNet: MR3857602
Digital Object Identifier: 10.1214/14-PS228

Primary: 60K35
Secondary: 82B20

Keywords: Abelian sandpile , burning bijection , chip-firing , height probabilities , Loop-erased random walk , Uniform spanning tree , Wilson’s algorithm

Vol.15 • 2018
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