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

Abstract

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.

49 pages, 2 figures, companion paper to arXiv:1306.2521, in this version minor technical gaps in the iteration arguments have been closed and some typos have been removed

References in corpus (4)

• Random walks on supercritical percolation clusters
• Invariance principle for the random conductance model with unbounded conductances
• Anomalous heat-kernel decay for random walk among bounded random conductances
• On symmetric random walks with random conductances on ${\mathbb{Z}}^d$

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