Brownian motion on stable looptrees

Archer, Eleanor

doi:10.1214/20-aihp1103

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2022

2024

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Cited by 4 publications

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“…This result then transfers to the SRW sequence in place of by standard arguments using the strong law of large numbers and continuity of the limit process. We refer to [ 5 , Section 4.2] for an example of such an argument. …”

Section: Introductionmentioning

confidence: 99%

The GHP Scaling Limit of Uniform Spanning Trees in High Dimensions

Archer,

Nachmias,

Shalev

2024

Commun. Math. Phys.

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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 $${\mathbb {Z}}_n^d$$ Z n d with $$d>4$$ d > 4 , the hypercube $$\{0,1\}^n$$ { 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.

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