The GHP Scaling Limit of Uniform Spanning Trees in High Dimensions

Eleanor Archer*, Asaf Nachmias, Matan Shalev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We show that the Brownian continuum random tree is the Gromov–Hausdorff–Prohorov scaling limit of the uniform spanning tree on high-dimensional graphs including the d-dimensional torus Znd with d>4, the hypercube {0,1}n, and transitive expander graphs. Several corollaries for associated quantities are then deduced: convergence in distribution of the rescaled diameter, height and simple random walk on these uniform spanning trees to their continuum analogues on the continuum random tree.

Original languageEnglish
Article number73
JournalCommunications in Mathematical Physics
Volume405
Issue number3
DOIs
StatePublished - Mar 2024

Funding

FundersFunder number
European Research Council101001124, 676970
Israel Science Foundation1294/19

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