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arXiv · 1110.4523

Minimal configurations and sandpile measures

Antal A. Jarai·Nicolas Werning
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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.

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Antal A. Jarai, Nicolas Werning. 2012-06-19. Minimal configurations and sandpile measures. https://doi.org/10.1007/s10959-012-0446-z

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