The local limit of uniform spanning trees

Asaf Nachmias; Yuval Peres

doi:10.1007/s00440-021-01072-2

The local limit of uniform spanning trees

Asaf Nachmias, Yuval Peres

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	1133-1161
Number of pages	29
Journal	Probability Theory and Related Fields
Volume	182
Issue number	3-4
DOIs	https://doi.org/10.1007/s00440-021-01072-2
State	Published - Apr 2022

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/s00440-021-01072-2

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title = "The local limit of uniform spanning trees",

abstract = "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.",

author = "Asaf Nachmias and Yuval Peres",

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The local limit of uniform spanning trees

Abstract

All Science Journal Classification (ASJC) codes

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