The diameter of uniform spanning trees in high dimensions

Peleg Michaeli*, Asaf Nachmias, Matan Shalev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We show that the diameter of a uniformly drawn spanning tree of a connected graph on n vertices which satisfies certain high-dimensionality conditions typically grows like Θ(n). In particular this result applies to expanders, finite tori Zmd of dimension d≥ 5 , the hypercube { 0 , 1 } m, and small perturbations thereof.

Original languageEnglish
Pages (from-to)261-294
Number of pages34
JournalProbability Theory and Related Fields
Volume179
Issue number1-2
DOIs
StatePublished - Feb 2021

Funding

FundersFunder number
Horizon 2020 Framework Programme676970
European Research Council
Israel Science Foundation1207/15

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