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Consider a random walk on $\mathbb{Z}^d$ in a translation-invariant andergodic random environment and starting from the origin. In this short note,assuming that a quenched invariance principle for the opportunely-rescaledwalks holds, we show how to derive an $L^1$-convergence of the correspondingsemigroups. We then apply this result to obtain a quenched pathwisehydrodynamic limit for the simple symmetric exclusion process on$\mathbb{Z}^d$, $d\ge 2$, with i.i.d. symmetric nearest-neighbors conductances$\omega_{xy}\in [0,\infty)$ only satisfying $$\mathbb{Q}(\omega_{xy}>0)>p_c\,$$ where $p_c$ is the critical value for bond percolation.

From quenched invariance principle to semigroup convergence with applications to exclusion processes