Abelian sandpiles: an overview and results on certain transitive graphs (Q2906831)
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scientific article; zbMATH DE number 6077820
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Abelian sandpiles: an overview and results on certain transitive graphs |
scientific article; zbMATH DE number 6077820 |
Statements
5 September 2012
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abelian sandpiles
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burning algorithm
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uniform spanning forest
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infinite volume limit
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transitive graph
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bounded harmonic function
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math.PR
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Abelian sandpiles: an overview and results on certain transitive graphs (English)
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In the framework of probability models on graphs, this paper presents a review of the abelian sandpile model with a special emphasis on the Majumdar-Dhar bijection which is used to extend some results on the infinite volume limit of the model defined on certain transitive graphs. Detailed results are reviewed for wired spanning forest and transitive graphs with some special volume growth. The theoretical derivations work mainly via Wilson's method.
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