Invariance principle for the random conductance model with unbounded conductances

We study a continuous time random walk $X$ in an environment of i.i.d. random conductances ${\mu }_e\in [1,\mathrm{\infty })$. We obtain heat kernel bounds and prove a quenched invariance principle for $X$. This holds even when $\mathbb{E}{\mu }_e=\mathrm{\infty }$.