The Transition Probability of the q-TAZRP (q-Bosons) with Inhomogeneous Jump Rates
In this paper we consider the q-deformed totally asymmetric zero range process (q-TAZRP), also known as the q-boson (stochastic) particle system, on the Z lattice, such that the jump rate of a particle depends on the site where it is on the lattice. We derive the transition probability for an n part...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2016 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2016
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147736 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The Transition Probability of the q-TAZRP (q-Bosons) with Inhomogeneous Jump Rates / D. Wang, D. Waugh // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 19 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862620751346008064 |
|---|---|
| author | Wang, D. Waugh, D. |
| author_facet | Wang, D. Waugh, D. |
| citation_txt | The Transition Probability of the q-TAZRP (q-Bosons) with Inhomogeneous Jump Rates / D. Wang, D. Waugh // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 19 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper we consider the q-deformed totally asymmetric zero range process (q-TAZRP), also known as the q-boson (stochastic) particle system, on the Z lattice, such that the jump rate of a particle depends on the site where it is on the lattice. We derive the transition probability for an n particle process in Bethe ansatz form as a sum of n! n-fold contour integrals. Our result generalizes the transition probability formula by Korhonen and Lee for q-TAZRP with a homogeneous lattice, and our method follows the same approach as theirs.
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| first_indexed | 2025-12-07T13:22:50Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147736 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T13:22:50Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Wang, D. Waugh, D. 2019-02-15T18:55:25Z 2019-02-15T18:55:25Z 2016 The Transition Probability of the q-TAZRP (q-Bosons) with Inhomogeneous Jump Rates / D. Wang, D. Waugh // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 19 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 82B23; 82C22; 60J35 DOI:10.3842/SIGMA.2016.037 https://nasplib.isofts.kiev.ua/handle/123456789/147736 In this paper we consider the q-deformed totally asymmetric zero range process (q-TAZRP), also known as the q-boson (stochastic) particle system, on the Z lattice, such that the jump rate of a particle depends on the site where it is on the lattice. We derive the transition probability for an n particle process in Bethe ansatz form as a sum of n! n-fold contour integrals. Our result generalizes the transition probability formula by Korhonen and Lee for q-TAZRP with a homogeneous lattice, and our method follows the same approach as theirs. This paper is a contribution to the Special Issue on Asymptotics and Universality in Random Matrices,
 Random Growth Processes, Integrable Systems and Statistical Physics in honor of Percy Deift and Craig Tracy.
 The full collection is available at http://www.emis.de/journals/SIGMA/Deift-Tracy.html.
 s
 The authors are indebted to Ivan Corwin for numerous comments, especially on the relation to
 the spectral theory and on the proof of Corollary 1.3. We also thank Eunghyun Lee for valuable
 suggestions and comments. At last, we thank the anonymous referees for their comments,
 suggestions and corrections, especially on a sign error in the manuscript. The first named
 author is supported partially by the startup grant R-146-000-164-133. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Transition Probability of the q-TAZRP (q-Bosons) with Inhomogeneous Jump Rates Article published earlier |
| spellingShingle | The Transition Probability of the q-TAZRP (q-Bosons) with Inhomogeneous Jump Rates Wang, D. Waugh, D. |
| title | The Transition Probability of the q-TAZRP (q-Bosons) with Inhomogeneous Jump Rates |
| title_full | The Transition Probability of the q-TAZRP (q-Bosons) with Inhomogeneous Jump Rates |
| title_fullStr | The Transition Probability of the q-TAZRP (q-Bosons) with Inhomogeneous Jump Rates |
| title_full_unstemmed | The Transition Probability of the q-TAZRP (q-Bosons) with Inhomogeneous Jump Rates |
| title_short | The Transition Probability of the q-TAZRP (q-Bosons) with Inhomogeneous Jump Rates |
| title_sort | transition probability of the q-tazrp (q-bosons) with inhomogeneous jump rates |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147736 |
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