Type

Journal Article

Authors

V. B. Priezzhev
A. M. Povolotsky
T. C. Dorlas

Subjects

Mathematics

Topics
current behavior probability scaling particles form survival large scale

From Vicious Walkers to TASEP (2008)

Abstract We propose a model of semi-vicious walkers, which interpolates between the totally asymmetric simple exclusion process and the vicious walkers model, having the two as limiting cases. For this model we calculate the asymptotics of the survival probability for m particles and obtain a scaling function, which describes the transition from one limiting case to another. Then, we use a fluctuation-dissipation relation allowing us to reinterpret the result as the particle current generating function in the totally asymmetric simple exclusion process. Thus we obtain the particle current distribution asymptotically in the large time limit as the number of particles is fixed. The results apply to the large deviation scale as well as to the diffusive scale. In the latter we obtain a new universal distribution, which has a skew non-Gaussian form. For m particles its asymptotic behavior is shown to be e^(-(y^2)/(2m^2)) as y → −∞ and e^(-(y^2)/(2m))*y^(-(m(m-1))/2) as y → ∞.
Collections Ireland -> DAIR -> Type = Article
Ireland -> DAIR -> Status = Published

Full list of authors on original publication

V. B. Priezzhev, A. M. Povolotsky, T. C. Dorlas

Experts in our system

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T. C. Dorlas
DAIR
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