We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. We prove an invariance principle (functional central limit theorem) under almost every fixed environment. The assumptions are nonnestling, at least two spatial dimensions, and a 2+ɛ moment for the step of the walk uniformly in the environment. The main point behind the invariance principle is that the quenched mean of the walk behaves subdiffusively.
"Quenched invariance principle for multidimensional ballistic random walk in a random environment with a forbidden direction." Ann. Probab. 35 (1) 1 - 31, January 2007. https://doi.org/10.1214/009117906000000610