Einstein relation for random walks in random environments

We consider a tracer particle performing a nearest neighbor random walk on in dimension d[greater-or-equal, slanted]3 with random jump rates. This kind of a walk models the motion of a charged particle under a constant external electric field. We assume that the jump rates admit only two values 0<[gamma]-<[gamma]+<+[infinity], representing the lower and upper conductivities. We prove the existence of the mobility coefficient and that it equals to the diffusivity coefficient of the particle in zero external field.