English

The local limit of uniform spanning trees

Probability 2020-11-18 v1

Abstract

We show that the local limit of the uniform spanning tree on any finite, simple, connected, regular graph sequence with degree tending to infinity is the Poisson(1) branching process conditioned to survive forever. An extension to "almost" regular graphs and a quenched version are also given.

Keywords

Cite

@article{arxiv.2011.08833,
  title  = {The local limit of uniform spanning trees},
  author = {Asaf Nachmias and Yuval Peres},
  journal= {arXiv preprint arXiv:2011.08833},
  year   = {2020}
}

Comments

25 pages

R2 v1 2026-06-23T20:19:28.487Z