Ballistic random walks in random environment at low disorder

We consider random walks in a random environment of the type p(0) + gammaxiz, where p(0) denotes the transition probabilities of a stationary random walk on Z(d), to nearest neighbors, and xi(Z) is an i.i.d. random perturbation. We give an explicit expansion, for small gamma, of the asymptotic speed of the random walk under the annealed law, up to order 2. As an application, we construct, in dimension d greater than or equal to 2, a walk which goes faster than the stationary walk under the mean environment.