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 |
| Main Authors: | , |
| 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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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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| Summary: | 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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| ISSN: | 1815-0659 |