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We consider a ballistic random walk in an i.i.d. random environment that doesnot allow retreating in a certain fixed direction. We prove an invarianceprinciple (functional central limit theorem) under almost every fixedenvironment. The assumptions are nonnestling, at least two spatial dimensions,and a $2+\epsilon$ moment for the step of the walk uniformly in theenvironment. The main point behind the invariance principle is that thequenched mean of the walk behaves subdiffusively.

Quenched invariance principle for multidimensional ballistic random walk in a random environment with a forbidden direction