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Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles
Eunghyun Lee, Temirlan Raimbekov Department of Mathematics, Nazarbayev University, Nur-sultan, Kazakhstan
Abstract:
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 $S_N$. On other hand, the transition probabilities of the multi-species ASEP, in general, may be expressed as a sum of much more terms than $N!$. In this paper, we show that if the initial order of species is given by $2\cdots 21$, $12\cdots 2$, $1\cdots 12$ or $21\cdots 1$, then the transition probabilities can be expressed as a sum of at most $N!$ contour integrals, and provide their formulas explicitly.
Keywords:
multi-species ASEP, transition probability, Bethe ansatz, symmetric group.
Received: April 15, 2021; in final form January 24, 2022; Published online January 29, 2022
Citation:
Eunghyun Lee, Temirlan Raimbekov, “Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles”, SIGMA, 18 (2022), 008, 24 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1803 https://www.mathnet.ru/eng/sigma/v18/p8
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Abstract page: | 45 | Full-text PDF : | 20 | References: | 8 |
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