On the TASEP with Second Class Particles

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...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2018
Main Author: Lee, E.
Format: Article
Language:English
Published: Інститут математики НАН України 2018
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/209458
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:On the TASEP with Second Class Particles / E. Lee // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 18 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-209458
record_format dspace
spelling Lee, E.
2025-11-21T19:13:37Z
2018
On the TASEP with Second Class Particles / E. Lee // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 18 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 60J25; 60K35; 82B23
arXiv: 1705.10544
https://nasplib.isofts.kiev.ua/handle/123456789/209458
https://doi.org/10.3842/SIGMA.2018.006
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×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].
This work was supported by the social policy grant from Nazarbayev University. The author is grateful to the anonymous referees for valuable comments and suggestions.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
On the TASEP with Second Class Particles
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title On the TASEP with Second Class Particles
spellingShingle On the TASEP with Second Class Particles
Lee, E.
title_short On the TASEP with Second Class Particles
title_full On the TASEP with Second Class Particles
title_fullStr On the TASEP with Second Class Particles
title_full_unstemmed On the TASEP with Second Class Particles
title_sort on the tasep with second class particles
author Lee, E.
author_facet Lee, E.
publishDate 2018
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description 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×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].
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/209458
citation_txt On the TASEP with Second Class Particles / E. Lee // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 18 назв. — англ.
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