Minimal Configurations and Sandpile Measures

Antal A. Járai () and Nicolás Werning ()
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Antal A. Járai: University of Bath
Nicolás Werning: University of Reading

Journal of Theoretical Probability, 2014, vol. 27, issue 1, 153-167

Abstract: Abstract We give a new simple construction of the sandpile measure on an infinite graph G, under the sole assumption that each tree in the Wired Uniform Spanning Forest on G has one end almost surely. For the so-called generalized minimal configurations, the limiting probability on G exists even without this assumption. We also give determinantal formulas for minimal configurations on general graphs in terms of the transfer current matrix.

Keywords: Abelian sandpile; Sandpile measure; Minimal configuration; Uniform spanning tree; Determinantal process; 60K35; 82C20 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10959-012-0446-z

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