Minimal configurations and sandpile measures
Probability
2014-03-13 v2
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
Cite
@article{arxiv.1110.4523,
title = {Minimal configurations and sandpile measures},
author = {Antal A. Jarai and Nicolas Werning},
journal= {arXiv preprint arXiv:1110.4523},
year = {2014}
}
Comments
16 pages; the introduction has been expanded and minor corrections have been made