Cluster size distributions in particle systems with asymmetric dynamics

Details Cluster size distributions in particle systems with asymmetric dynamics Cluster size distributions in particle systems with asymmetric dynamics

2001-09-27

arxiv.org/abs/cond-mat/0109515v1

Physical Review E 64, 056114 (2001)

Physics

Condensed Matter

Statistical Mechanics

12 pages, 3 figures, RevTeX

Scientific paper

10.1103/PhysRevE.64.056114

We present exact and asymptotic results for clusters in the one-dimensional totally asymmetric exclusion process (TASEP) with two different dynamics. The expected length of the largest cluster is shown to diverge logarithmically with increasing system size for ordinary TASEP dynamics and as a logarithm divided by a double logarithm for generalized dynamics, where the hopping probability of a particle depends on the size of the cluster it belongs to. The connection with the asymptotic theory of extreme order statistics is discussed in detail. We also consider a related model of interface growth, where the deposited particles are allowed to relax to the local gravitational minimum.

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