Quenched invariance principles for the random conductance model on a random graph with degenerate ergodic weights

Abstract

We consider a stationary and ergodic random field $\{\omega (e):e\in E_d\}$ that is parameterized by the edge set of the Euclidean lattice ${\mathbb{Z}}^d$, $d\ge 2$. The random variable $\omega (e)$, taking values in $[0,\infty )$ and satisfying certain moment bounds, is thought of as the conductance of the edge $e$. Assuming that the set of edges with positive conductances give rise to a unique infinite cluster ${\mathcal{C}}_{\infty }(\omega )$, we prove a quenched invariance principle for the continuous-time random walk among random conductances under relatively mild conditions on the structure of the infinite cluster. An essential ingredient of our proof is a new anchored relative isoperimetric inequality.

22 pages

References in corpus (2)

• Random walks on supercritical percolation clusters
• Invariance principle for the random conductance model with unbounded conductances

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