TY - JOUR

T1 - Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles

AU - Lee, Eunghyun

AU - Raimbekov, Temirlan

N1 - Funding Information:
This work was supported by the faculty development competitive research grants (090118FD5341 and 021220FD4251) by Nazarbayev University. We are thankful to Kamila Izhanova for assisting in preparation for the manuscript and to Francesco Sica for valuable comments. Most of all, we deeply appreciate anonymous referees for providing valuable comments to improve the earlier version of this paper.
Publisher Copyright:
© 2022, Institute of Mathematics. All rights reserved.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - Bethe ansatz

KW - Multi-species ASEP

KW - Symmetric group

KW - Transition probability

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U2 - 10.3842/SIGMA.2022.008

DO - 10.3842/SIGMA.2022.008

M3 - Article

AN - SCOPUS:85123624178

SN - 1815-0659

VL - 18

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

M1 - 008

ER -