Let $X, X_1, X_2, \dots $ be a sequence of nondegenerate, independent and identically distributed random variables and set $S_n=X_1+\dots +X_n$,  $V_n^2=X_1^2+\dots +X_n^2$. We answer a question of Gotze, Gine and Mason by providing a simple necessary and sufficient condition…

We prove that random walks in i.i.d. random environments which oscillate in a given direction have velocity zero with respect to that direction. This complements existing results thus giving a general law of large numbers under the only assumption of…