The local limit of uniform spanning trees

Asaf Nachmias, Yuval Peres

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish
Pages (from-to)1133-1161
Number of pages29
JournalProbability Theory and Related Fields
Issue number3-4
StatePublished - Apr 2022

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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