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 …

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 …

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 …

Growth exponent for loop-erased random walk in three dimensions Page 1 The Annals of
Probability 2018, Vol. 46, No. 2, 687–774 https://doi.org/10.1214/16-AOP1165 © Institute of …

We establish scaling limits for the random walk whose state space is the range of a simple
random walk on the four-dimensional integer lattice. These concern the asymptotic …

We prove CLTs for biased randomly trapped random walks in one dimension. By
considering a sequence of regeneration times, we will establish an annealed invariance …

We derive sub-Gaussian bounds for the annealed transition density of the simple random
walk on a high-dimensional loop-erased random walk. The walk dimension that appears in …

In this article, a localisation result is proved for the biased random walk on the range of a
simple random walk in high dimensions (d ≥ 5). This demonstrates that, unlike in the …

We provide conditions that classify sequences of random graphs into two types in terms of
cover times. One type (type 1) is the class of random graphs on which the cover times are of …