We give a unified treatment of the limit, as the size tends to infinity, of random simply
generated trees, including both the well-known result in the standard case of critical Galton …

We consider stochastic processes on complete, locally compact tree-like metric spaces (T,r)
on their “natural scale” with boundedly finite speed measure ν. Given a triple (T,r,ν) such a …

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 …

The first main result of this paper is that the law of the (rescaled) two-dimensional uniform
spanning tree is tight in a space whose elements are measured, rooted real trees …

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 …

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 …

Under the assumption that sequences of graphs equipped with resistances, associated
measures, walks and local times converge in a suitable Gromov-Hausdorff topology, we …

The real trees form a class of metric spaces that extends the class of trees with edge lengths
by allowing behavior such as locally infinite total edge length and vertices with infinite …

We establish conditions on sequences of graphs which ensure that the mixing times of the
random walks on the graphs in the sequence converge. The main assumption is that the …

We study here a detailed conjecture regarding one of the most important cases of
anomalous diffusion, ie, the behavior of the “ant in the labyrinth.” It is natural to conjecture …