The main theme of these lecture notes is to analyze heat conduction on disordered media
such as fractals and percolation clusters by means of both probabilistic and analytic …

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 …

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 …

In this work, it is proved that the set of boundedly-compact pointed metric spaces, equipped
with the Gromov–Hausdorff topology, is a Polish space. The same is done for the Gromov …

We present a new general framework for metrization of Gromov-Hausdorff-type topologies
on non-compact metric spaces. We also give easy-to-check conditions for separability and …

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

We show that the Gromov-Hausdorff-Prohorov scaling limit of a critical percolation cluster on
a random hyperbolic triangulation of the half-plane is the Brownian continuum random tree …

We study the asymptotic behavior of the exit times of random walk from Euclidean balls
around the origin of the incipient infinite cluster in a manner inspired by Kumagai and …

Via a Dirichlet form extension theorem and making full use of two-sided heat kernel
estimates, we establish quenched invariance principles for random walks in random …