Superdiffusivity of asymmetric exclusion process in dimensions one and two

C. Landim, J. Quastel, M. Salmhofer, H.T. Yau

We prove that the diffusion coefficient of the asymmetric exclusion process diverges at least as fast as $t^{1/4}$ in dimension $d=1$ and $(\log t)^{1/2}$ in $d=2$. The method applies to nearest and non-nearest neighbor asymmetric exclusion processes.