  We consider random walks in i.i.d. elliptic random environments which are not
uniformly elliptic. We introduce a computable condition in dimension $d=2$ and
a general condition valid for dimensions $d\ge 2$ expressed in terms of the
exit time from a box, which ensure that local trapping would not inhibit a
ballistic behavior of the random walk. An important technical innovation
related to our computable condition, is the introduction of a geometrical point
of view to classify the way in which the random walk can become trapped, either
in an edge, a wedge or a square. Furthermore, we prove that the general
condition we introduce is sharp.

Probability