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

Eunghyun Lee, Temirlan Raimbekov

Symmetry Integrability and Geometry Methods and Applications, 2022

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DOI 10.3842/sigma.2022.008

Data confidence 70 medium

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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 2then the transition probabilities can be expressed as a sum of at most N !contour integrals, and provide their formulas explicitly.