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arXiv · 1011.0196

Inter-particle gap distribution and spectral rigidity of totally asymmetric simple exclusion process with open boundaries

Milan Krbalek·Pavel Hrabak
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Abstract

We consider the one-dimensional totally asymmetric simple exclusion model (TASEP model) with open boundary conditions and present the analytical computations leading to the exact formula for distance clearance distribution, i.e. probability density for a clear distance between subsequent particles of the model. The general relation is rapidly simplified for middle part of the one-dimensional lattice using the large $N$ approximation. Both the analytical formulas and their approximations are successfully compared with the numerical representation of the TASEP model. Furthermore, we introduce the pertinent estimation for so-called spectral rigidity of the model. The results obtained are sequentially discussed within the scope of vehicular traffic theory.

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Milan Krbalek, Pavel Hrabak. 2010-10-31. Inter-particle gap distribution and spectral rigidity of totally asymmetric simple exclusion process with open boundaries. https://doi.org/10.1088/1751-8113%2F44%2F17%2F175203

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