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

Symmetry Integrability and Geometry-Methods and Applications

article

Eunghyun LeeTemirlan Raimbekov¹ 

[1] Department of Mathematics, Nazarbayev University

关键词: multi-species ASEP;    transition probability;    Bethe ansatz;    symmetric group.;   

DOI  :  10.3842/SIGMA.2022.008

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown