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arXiv · 2104.06471

Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles

Eunghyun Lee·Temirlan Raimbekov
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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.

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Eunghyun Lee, Temirlan Raimbekov. 2021-04-13. Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles. https://doi.org/10.3842/sigma.2022.008

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