Order of current variance and diffusivity in the asymmetric simple   exclusion process
  We prove that the variance of the current across a characteristic is of order t^{2/3} in a stationary asymmetric simple exclusion process, and that the diffusivity has order t^{1/3}. The proof proceeds via couplings to show the corresponding results for the expected deviations and variance of a second class particle. 
Marton Balazs and Timo Seppalainen