Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles
Lee E. Raimbekov T.
2022Institute of Mathematics
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
2022#18
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 SN . 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 · · · 21, 12 · · · 2, 1 · · · 12 or 21 · · · 1, then the transition probabilities can be expressed as a sum of at most N! contour integrals, and provide their formulas explicitly.
Bethe ansatz , Multi-species ASEP , Symmetric group , Transition probability
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Department of Mathematics, Nazarbayev University, Nursultan, Kazakhstan
Department of Mathematics
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