Random walks in random Dirichlet environment are transient in dimension d ≥ 3. Probab. Theory Relat. Fields 151, nos

Abstract: We consider random walks in random Dirichlet environment (RWDE) which is a special type of random walks in random environment where the exit prob-abilities at each site are i.i.d. Dirichlet random variables. On Zd, RWDE are parame-terized by a 2d-uplet of positive reals. We prove that for all values of the parameters, RWDE are transient in dimension d ≥ 3. We also prove that the Green function has some finite moments and we characterize the finite moments. Our result is more gen-eral and applies for example to finitely generated transient Cayley graphs. In terms of reinforced random walks it implies that linearly edge-oriented reinforced random walks are transient for d ≥ 3. 1