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 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 …

This article studies potential theory and spectral analysis on compact metric spaces, which
we refer to as fractal quantum graphs. These spaces can be represented as a (possibly …

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 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 …

In this article, we study a simple random walk on a decorated Galton-Watson tree, obtained
from a Galton-Watson tree by replacing each vertex of degree $ n $ with an independent …

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 …

We present results concerning the behavior of random walks and diffusions on disordered
media. Examples treated include fractals and various models of random graphs, such as …

In this article, universal concentration estimates are established for the local times of random
walks on weighted graphs in terms of the resistance metric. As a particular application of …