Harnack inequalities on weighted graphs and some applications to the random conductance model

Sebastian Andres, Jean-Dominique Deuschel, Martin Slowik

Published 2013-12-19, updated 2014-09-04Version 2

We establish elliptic and parabolic Harnack inequalities on graphs with unbounded weights. As an application we prove a local limit theorem for a continuous time random walk $X$ in an environment of ergodic random conductances taking values in $[0, \infty)$ satisfying some moment conditions.