Ballistic Random Walk in a Random Environment with a Forbidden Direction

We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. Homogenization and regeneration techniques combine to prove a law of large numbers and an averaged invariance principle. The assumptions are non-nestling and $1+\text{e}$ (resp.
$2+\text{e}$) moments for the step of the walk uniformly in the environment, for the law of large numbers (resp. invariance principles). We also investigate invariance principles under fixed environments, and invariance principles for the environment-dependent mean of the walk.