The Annals of Applied Probability

Behavior dominated by slow particles in a disordered asymmetric exclusion process

Ilie Grigorescu, Min Kang, and Timo Seppäläinen

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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 rates attached to the particles. When slow particles are sufficiently rare, the system has a phase transition. At low densities there are no equilibrium distributions, and on the hydrodynamic scale the initial profile is transported rigidly. We elaborate this situation further by finding the correct order of the correction from the hydrodynamic limit, together with distributional bounds averaged over the disorder. We consider two settings, a macroscopically constant low density profile and the outflow from a large jam.

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Ann. Appl. Probab., Volume 14, Number 3 (2004), 1577-1602.

First available in Project Euclid: 13 July 2004

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Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Asymmetric exclusion process hydrodynamic limit random rates


Grigorescu, Ilie; Kang, Min; Seppäläinen, Timo. Behavior dominated by slow particles in a disordered asymmetric exclusion process. Ann. Appl. Probab. 14 (2004), no. 3, 1577--1602. doi:10.1214/105051604000000387.

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