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Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {Eunghyun Lee and Temirlan Raimbekov},
     title = {Simplified {Forms} of the {Transition} {Probabilities} of the {Two-Species} {ASEP} with {Some} {Initial} {Orders} of {Particles}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a7/}
}
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Eunghyun Lee; Temirlan Raimbekov. Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a7/

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