Zero Range Process and Multi-Dimensional Random Walks
The special limit of the totally asymmetric zero range process of the low-dimensional non-equilibrium statistical mechanics described by the non-Hermitian Hamiltonian is considered. The calculation of the conditional probabilities of the model are based on the algebraic Bethe ansatz approach. We dem...
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| Дата: | 2017 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2017
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148588 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Zero Range Process and Multi-Dimensional Random Walks / N.M Bogoliubov, C. Malyshev // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 32 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-148588 |
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irk-123456789-1485882019-02-19T01:31:30Z Zero Range Process and Multi-Dimensional Random Walks Bogoliubov, N.M. Malyshev, C. The special limit of the totally asymmetric zero range process of the low-dimensional non-equilibrium statistical mechanics described by the non-Hermitian Hamiltonian is considered. The calculation of the conditional probabilities of the model are based on the algebraic Bethe ansatz approach. We demonstrate that the conditional probabilities may be considered as the generating functions of the random multi-dimensional lattice walks bounded by a hyperplane. This type of walks we call the walks over the multi-dimensional simplicial lattices. The answers for the conditional probability and for the number of random walks in the multi-dimensional simplicial lattice are expressed through the symmetric functions. 2017 Article Zero Range Process and Multi-Dimensional Random Walks / N.M Bogoliubov, C. Malyshev // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 32 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 05A19; 05E05; 82B23 DOI:10.3842/SIGMA.2017.056 http://dspace.nbuv.gov.ua/handle/123456789/148588 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The special limit of the totally asymmetric zero range process of the low-dimensional non-equilibrium statistical mechanics described by the non-Hermitian Hamiltonian is considered. The calculation of the conditional probabilities of the model are based on the algebraic Bethe ansatz approach. We demonstrate that the conditional probabilities may be considered as the generating functions of the random multi-dimensional lattice walks bounded by a hyperplane. This type of walks we call the walks over the multi-dimensional simplicial lattices. The answers for the conditional probability and for the number of random walks in the multi-dimensional simplicial lattice are expressed through the symmetric functions. |
| format |
Article |
| author |
Bogoliubov, N.M. Malyshev, C. |
| spellingShingle |
Bogoliubov, N.M. Malyshev, C. Zero Range Process and Multi-Dimensional Random Walks Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Bogoliubov, N.M. Malyshev, C. |
| author_sort |
Bogoliubov, N.M. |
| title |
Zero Range Process and Multi-Dimensional Random Walks |
| title_short |
Zero Range Process and Multi-Dimensional Random Walks |
| title_full |
Zero Range Process and Multi-Dimensional Random Walks |
| title_fullStr |
Zero Range Process and Multi-Dimensional Random Walks |
| title_full_unstemmed |
Zero Range Process and Multi-Dimensional Random Walks |
| title_sort |
zero range process and multi-dimensional random walks |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148588 |
| citation_txt |
Zero Range Process and Multi-Dimensional Random Walks / N.M Bogoliubov, C. Malyshev // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 32 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT bogoliubovnm zerorangeprocessandmultidimensionalrandomwalks AT malyshevc zerorangeprocessandmultidimensionalrandomwalks |
| first_indexed |
2023-05-20T17:30:53Z |
| last_indexed |
2023-05-20T17:30:53Z |
| _version_ |
1796153470662737920 |