Law of large numbers for the asymmetric simple exclusion process
arXiv:math/0305174 · doi:10.1016/j.spa.2004.04.003
Abstract
We consider simple exclusion processes on Z for which the underlying random walk has a finite first moment and a non-zero mean and whose initial distributions are product measures with different densities to the left and to the right of the origin. We prove a strong law of large numbers for the number of particles present at time t in an interval growing linearly with t.
16 pages