2014/01/01 by Samuel L. Gamlin, Samuel Gamlin, Antal A. Járai
Mathematics · Physics and Astronomy · #Bijection #Bijection, injection and surjection #Combinatorics #Computer science #Discrete mathematics #Graph #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Measure (data warehouse) #Spanning tree #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Tree (set theory) #Upper and lower bounds #math.PR #msc:60K35
paper · pdf · doi:10.1214/ejp.v19-3542
published as Electron. J. Probab. vol.19, no. 117 (2014) · 26 pages; 1 EPS figure. Minor alterations made after comments from referee
openalex publication_date 2014/01/01 · arxiv created 2014/08/07 · arxiv updated 2014/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.