Law of large numbers for the asymmetric simple exclusion process

E. Andjel, P. A. Ferrari, A. Siqueira

Published 2003-05-12Version 1

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.