Minimal Configurations and Sandpile Measures

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 th...

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Bibliographic Details
Published in:Journal of theoretical probability 2014-03, Vol.27 (1), p.153-167
Main Authors: Járai, Antal A., Werning, Nicolás
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
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Summary: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.
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-012-0446-z