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We consider the random conductance model in a stationary and ergodicenvironment. Under suitable moment conditions on the conductances and theirinverse, we prove a quenched invariance principle for the random walk among therandom conductances. The moment conditions improve earlier results of Andres,Deuschel and Slowik [Ann.\ Probab.] and are the minimal requirement to ensurethat the corrector is sublinear everywhere. The key ingredient is anessentially optimal deterministic local boundedness result for finitedifference equations in divergence form.

Quenched invariance principle for random walks among random degenerate conductances