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 $\mathbb{Z}^d$,$d \geq 2$. The random variable $\omega(e)$, taking values in $[0, \infty)$ andsatisfying 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 aunique infinite cluster $\mathcal{C}_{\infty}(\omega)$, we prove a quenchedinvariance principle for the continuous-time random walk among randomconductances under relatively mild conditions on the structure of the infinitecluster. An essential ingredient of our proof is a new anchored relativeisoperimetric inequality.
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机译：我们考虑由欧几里得格$ \ mathbb {Z} ^ d $，$ d \ geq 2的边集参数化的平稳且遍历遍历的随机字段$ \ {\ omega（e）：e \ in E_d \} $ $。随机变量$ \ omega（e）$的取值为$ [0，\ infty）$，并且满足一定的矩范围，被认为是边$ e $的电导。假设具有正电导的边集产生唯一的无限簇$ \ mathcal {C} _ {\ infty}（\ omega）$，我们证明了在相对温和条件下随机电导的连续时间随机游动的淬灭不变原理在无限集群的结构上。我们证明的重要组成部分是新的锚定相对等距不等式。
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