Shock fluctuations in asymmetric simple exclusion

Summary The one dimensional nearest neighbors asymmetric simple exclusion process in used as a microscopic approximation to the Burgers equation. We study the process with rates of jumpsp>q to the right and left, respectively, and with initial product measure with densities < to the left and right of the origin, respectively (with shock initial conditions). We prove that a second class particle added to the system at the origin at time zero identifies microscopically the shock for all later times. If this particle is added at another site, then it describes the behavior of a characteristic of the Burgers equation. For vanishing left density (=0) we prove, in the scale t^1/2, that the position of the shock at timet depends only on the initial configuration in a region depending ont. The proofs are based on laws of large numbers for the second class particle.