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On the TASEP with Second Class Particles
Symmetry, integrability and geometry: methods and applications, Tome 14 (2018) Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we study some conditional probabilities for the totally asymmetric simple exclusion processes (TASEP) with second class particles. To be more specific, we consider a finite system with one first class particle and $N-1$ second class particles, and we assume that the first class particle is initially at the leftmost position. In this case, we find the probability that the first class particle is at $x$ and it is still the leftmost particle at time $t$. In particular, we show that this probability is expressed by the determinant of an $N\times N$ matrix of contour integrals if the initial positions of particles satisfy the step initial condition. The resulting formula is very similar to a known formula in the (usual) TASEP with the step initial condition which was used for asymptotics by Nagao and Sasamoto [Nuclear Phys. B 699 (2004), 487–502].
Keywords: TASEP; Bethe ansatz; second class particles. 
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     author = {Eunghyun Lee},
     title = {On the {TASEP} with {Second} {Class} {Particles}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a5/}
}
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Eunghyun Lee. On the TASEP with Second Class Particles. Symmetry, integrability and geometry: methods and applications, Tome 14 (2018). http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a5/

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