Minimal configurations and sandpile measures

Reference:

Jarai, A. A. and Werning, N., 2013. Forthcoming. Minimal configurations and sandpile measures. Journal of Theoretical Probability

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Official URL:

http://dx.doi.org/10.1007/s10959-012-0446-z

Related URLs:

• http://arxiv.org/abs/1110.4523v2

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 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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