A Note on the Diffusivity of Finite-range Asymmetric Exclusion Processes on Z

The diffusivity D(t) of finite-range asymmetric exclusion processes on Z with non-zero drift is expected to be of order t1/3. Seppäläinen and Balázs recently proved this conjecture for the nearest neighbor case. We extend their results to general finite range exclusion by proving that the Laplace transform of the diffusivity is of the conjectured order. We also obtain the correct order pointwise upper bound for D(t).