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 …

The mating of trees approach to Schramm–Loewner evolution (SLE) in the random
geometry of Liouville quantum gravity (LQG) has been recently developed by Duplantier et …

We establish that if a sequence of spaces equipped with resistance metrics and measures
converge with respect to the Gromov–Hausdorff-vague topology, and a certain non …

Given a sequence of resistance forms that converges with respect to the Gromov-Hausdorff-
vague topology and satisfies a uniform volume doubling condition, we show the …

In this paper, it is shown that if a sequence of resistance metric spaces equipped with
measures converges with respect to the local Gromov-Hausdorff-vague topology, and …

We show that the law of the three-dimensional uniform spanning tree (UST) is tight under
rescaling in a space whose elements are measured, rooted real trees, continuously …

We prove that the wired uniform spanning forest exhibits mean-field behaviour on a very
large class of graphs, including every transitive graph of at least quintic volume growth and …

We compute the precise logarithmic corrections to Alexander–Orbach behaviour for various
quantities describing the geometric and spectral properties of the four-dimensional uniform …

Self-similar Markov trees constitute a remarkable family of random compact real trees
carrying a decoration function that is positive on the skeleton. As the terminology suggests …

We extend the Aldous–Broder algorithm to generate the wired uniform spanning forests
(WUSFs) of infinite, transient graphs. We do this by replacing the simple random walk in the …