Minimal configurations and sandpile measures

Details Minimal configurations and sandpile measures Minimal configurations and sandpile measures

2011-10-20

arxiv.org/abs/1110.4523v1

Mathematics

Probability

13 pages

Scientific paper

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 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.

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