ar X iv : m at h / 06 05 26 6 v 1 [ m at h . PR ] 1 0 M ay 2 00 6 t 1 / 3 Superdiffusivity of Finite - Range Asymmetric Exclusion Processes
نویسندگان
چکیده
We consider finite-range asymmetric exclusion processes on Z with non-zero drift. The diffusivity D(t) is expected to be of O(t). We prove that D(t) ≥ Ct in the weak (Tauberian) sense that ∫∞ 0 e tD(t)dt ≥ Cλ 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) ≥ Ct(log t) in the usual sense.
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