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

Eunghyun Lee; Temirlan Raimbekov

doi:10.3842/SIGMA.2022.008

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

Eunghyun Lee, Temirlan Raimbekov

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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 · · · 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.

Original language	English
Article number	008
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	18
DOIs	https://doi.org/10.3842/SIGMA.2022.008
Publication status	Published - 2022

Keywords

Bethe ansatz
Multi-species ASEP
Symmetric group
Transition probability

ASJC Scopus subject areas

Geometry and Topology
Analysis
Mathematical Physics

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10.3842/SIGMA.2022.008

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title = "Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles",

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 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.",

keywords = "Bethe ansatz, Multi-species ASEP, Symmetric group, Transition probability",

author = "Eunghyun Lee and Temirlan Raimbekov",

note = "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: {\textcopyright} 2022, Institute of Mathematics. All rights reserved.",

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doi = "10.3842/SIGMA.2022.008",

language = "English",

volume = "18",

journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",

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

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

Abstract

Keywords

ASJC Scopus subject areas

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