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We study the large space and time scale behavior of a totally asymmetric,nearest-neighbor exclusion process in one dimension with random jump ratesattached to the particles. When slow particles are sufficiently rare the systemhas a phase transition. At low densities there are no equilibriumdistributions, and on the hydrodynamic scale the initial profile is transportedrigidly. We elaborate this situation further by finding the correct order ofthe correction from the hydrodynamic limit, together with distributional boundsaveraged over the disorder. We consider two settings, a macroscopicallyconstant low density profile and the outflow from a large jam.

Behavior dominated by slow particles in a disordered asymmetric exclusion process