We obtain Gaussian upper and lower bounds on the transition density qt (x, y) of the
continuous time simple random walk on a supercritical percolation cluster C_∞ in the …

In this work we principally study random walk on the supercritical infinite cluster for bond
percolation on ℤ d. We prove a quenched functional central limit theorem for the walk when …

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 …

Let (X, d, µ) be a metric measure space with a local regular Dirichlet form. We give
necessary and sufficient conditions for a parabolic Harnack inequality with global space …

We study a natural discrete Bochner-type inequality on graphs, and explore its merit as a
notion of “curvature” in discrete spaces. An appealing feature of this discrete version of the …

We give necessary and sufficient conditions for sub-Gaussian estimates of the heat kernel of
a strongly local regular Dirichlet form on a metric measure space. The conditions for two …

Characterization of subâ•’Gaussian heat kernel estimates on strongly recurrent graphs Page
1 Characterization of Sub-Gaussian Heat Kernel Estimates on Strongly Recurrent Graphs …

Given the variable-speed random walk on a weighted graph and a metric adapted to the
structure of the random walk, we construct a Brownian motion on a closely related metric …

We define sets with finitely ramified cell structure, which are generalizations of post-critically
finite self-similar sets introduced by Kigami and of fractafolds introduced by Strichartz. In …

In this paper, we consider symmetric jump processes of mixed-type on metric measure
spaces under general volume doubling condition, and establish stability of two-sided heat …