Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles
It has been known that the transition probability of the single-species ASEP with 𝑁 particles is expressed as a sum of 𝑁! 𝑁-fold contour integrals, which are related to permutations in the symmetric group 𝑆𝑁. On the other hand, the transition probabilities of the multi-species ASEP, in general, may...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2022 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2022
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211537 |
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| Cite this: | Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles. Eunghyun Lee and Temirlan Raimbekov. SIGMA 18 (2022), 008, 24 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859609522599886848 |
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| author | Lee, Eunghyun Raimbekov, Temirlan |
| author_facet | Lee, Eunghyun Raimbekov, Temirlan |
| citation_txt | Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles. Eunghyun Lee and Temirlan Raimbekov. SIGMA 18 (2022), 008, 24 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | It has been known that the transition probability of the single-species ASEP with 𝑁 particles is expressed as a sum of 𝑁! 𝑁-fold contour integrals, which are related to permutations in the symmetric group 𝑆𝑁. On the other hand, the transition probabilities of the multi-species ASEP, in general, may be expressed as a sum of many more terms than 𝑁!. In this paper, we show that if the initial order of species is given by 2⋯21, 12⋯2, 1⋯12, or 21⋯1, then the transition probabilities can be expressed as a sum of at most 𝑁! contour integrals, and provide their formulas explicitly.
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| first_indexed | 2026-03-14T04:17:20Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211537 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T04:17:20Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
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| spelling | Lee, Eunghyun Raimbekov, Temirlan 2026-01-05T12:29:33Z 2022 Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles. Eunghyun Lee and Temirlan Raimbekov. SIGMA 18 (2022), 008, 24 pages 1815-0659 https://doi.org/10.3842/SIGMA.2022.008 2020 Mathematics Subject Classification: 82C22; 60J27 arXiv:2104.06471 https://nasplib.isofts.kiev.ua/handle/123456789/211537 It has been known that the transition probability of the single-species ASEP with 𝑁 particles is expressed as a sum of 𝑁! 𝑁-fold contour integrals, which are related to permutations in the symmetric group 𝑆𝑁. On the other hand, the transition probabilities of the multi-species ASEP, in general, may be expressed as a sum of many more terms than 𝑁!. In this paper, we show that if the initial order of species is given by 2⋯21, 12⋯2, 1⋯12, or 21⋯1, then the transition probabilities can be expressed as a sum of at most 𝑁! contour integrals, and provide their formulas explicitly. This work was supported by the faculty development competitive research grants (090118FD5341 and 021220FD4251)by Nazarbayev University. We are thankful to Kamila Izhanova for assisting in the preparation of the manuscript and to Francesco Sica for valuable comments. Most of all, we deeply appreciate anonymous referees for providing valuable comments to improve the earlier version of this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles Article published earlier |
| spellingShingle | Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles Lee, Eunghyun Raimbekov, Temirlan |
| title | Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles |
| title_full | Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles |
| title_fullStr | Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles |
| title_full_unstemmed | Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles |
| title_short | Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles |
| title_sort | simplified forms of the transition probabilities of the two-species asep with some initial orders of particles |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211537 |
| work_keys_str_mv | AT leeeunghyun simplifiedformsofthetransitionprobabilitiesofthetwospeciesasepwithsomeinitialordersofparticles AT raimbekovtemirlan simplifiedformsofthetransitionprobabilitiesofthetwospeciesasepwithsomeinitialordersofparticles |