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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209458 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862654466931556352 |
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| author | Lee, E. |
| author_facet | Lee, E. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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].
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| first_indexed | 2025-12-02T00:39:27Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209458 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-02T00:39:27Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the TASEP with Second Class Particles Article published earlier |
| spellingShingle | On the TASEP with Second Class Particles Lee, E. |
| title | 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_short | On the TASEP with Second Class Particles |
| title_sort | on the tasep with second class particles |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209458 |
| work_keys_str_mv | AT leee onthetasepwithsecondclassparticles |