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arXiv · 1311.2388

The parallel TASEP, fixed particle number and weighted Motzkin paths

Marko Woelki
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Abstract

In this paper the totally asymmetric exclusion process (TASEP) with parallel update on an open lattice of size $L$ is considered in the maximum-current region. A formal expression for the generating function for the weight of configurations with $N$ particles is given. Further an interpretation in terms of $(u,l,d)$-colored weighted Motzkin paths is presented. Using previous results (Woelki and Schreckenberg 2009 {\it J. Stat. Mech} P05014, Woelki 2010 {\it Cellular Automata}, pp 637-645) the generating function is compared with the one for a possible 2nd-class particle dynamics for the parallel TASEP. It is shown that both become physically equivalent in the thermodynamic limit.

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Marko Woelki. 2013-11-11. The parallel TASEP, fixed particle number and weighted Motzkin paths. https://doi.org/10.1088/1751-8113%2F46%2F50%2F505003

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