un 2 00 6 t 1 / 3 Superdiffusivity of Finite - Range Asymmetric Exclusion Processes on Z Jeremy Quastel

We consider finite-range asymmetric exclusion processes on Z with non-zero drift. The diffusivity D(t) is expected to be of O(t1/3). We prove that D(t) ≥ Ct1/3 in the weak (Tauberian) sense that ∫∞ 0 e −λttD(t)dt ≥ Cλ−7/3 as λ → 0. The proof employs the resolvent method to make a direct comparison with the totally asymmetric simple exclusion process, for which the result is a consequence of the scaling limit for the two-point function recently obtained by Ferrari and Spohn. When p(z) ≥ p(−z) for each z > 0, we show further that tD(t) is monotone, and hence we can conclude that D(t) ≥ Ct1/3(log t)−7/3 in the usual sense.