We sharpen ellipticity criteria for random walks in i.i.d. random environments introduced by Campos and Ram\'{ \i}rez which ensure ballistic behavior. Furthermore, we construct new examples of random environments for which the walk satisfies the polynomial ballisticity criteria of Berger, Drewitz and Ram\'{ \i}rez. As a corollary, we can exhibit a new range of values for the parameters of Dirichlet random environments in dimension $d=2$ under which the corresponding random walk is ballistic.
Categories: math.PR