Anchored burning bijections on finite and infinite graphs

Samuel L. Gamlin, Antal A. Járai

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
145 Downloads (Pure)

Abstract

Let G be an infinite graph such that each tree in the wired uniform spanning forest on G has one end almost surely. On such graphs G, we give a family of continuous, measure preserving, almost one-to-one mappings from the wired spanning forest on G to recurrent sandpiles on G, that we call anchored burning bijections. In the special case of Zd, d≥2, we show how the anchored bijection, combined with Wilson’s stacks of arrows construction, as well as other known results on spanning trees, yields a power law upper bound on the rate of convergence to the sandpile measure along any exhaustion of Zd. We discuss some open problems related to these findings.

Original languageEnglish
Article number117
Pages (from-to)1-23
JournalElectronic Journal of Probability
Volume19
DOIs
Publication statusPublished - 16 Dec 2014

Keywords

  • Abelian sandpile
  • Burning algorithm
  • Loop-erased random walk
  • Uniform spanning tree
  • Wilson’s algorithm
  • Wired spanning forest

Fingerprint Dive into the research topics of 'Anchored burning bijections on finite and infinite graphs'. Together they form a unique fingerprint.

Cite this