TY - JOUR
T1 - Minimal configurations and sandpile measures
AU - Jarai, Antal A
AU - Werning, Nicolás
PY - 2014/3
Y1 - 2014/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84865277670&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1007/s10959-012-0446-z
UR - http://arxiv.org/abs/1110.4523v2
U2 - 10.1007/s10959-012-0446-z
DO - 10.1007/s10959-012-0446-z
M3 - Article
SN - 0894-9840
VL - 27
SP - 153
EP - 167
JO - Journal of Theoretical Probability
JF - Journal of Theoretical Probability
IS - 1
ER -