Minimal configurations and sandpile measures

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.

16 pages; the introduction has been expanded and minor corrections have been made

References in corpus (2)

• Chip-Firing and Rotor-Routing on Directed Graphs
• Abelian sandpiles: an overview and results on certain transitive graphs

Cited by in corpus (7)

• Interlacements and the Wired Uniform Spanning Forest
• Indistinguishability of Trees in Uniform Spanning Forests
• Wired Cycle-Breaking Dynamics for Uniform Spanning Forests
• Transfer current and pattern fields in spanning trees
• Anchored burning bijections on finite and infinite graphs
• Non-criticality criteria for Abelian sandpile models with sources and sinks
• Asymptotic height distribution in high-dimensional sandpiles