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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2017 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148588 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862707125930688512 |
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| author | Bogoliubov, N.M. Malyshev, C. |
| author_facet | Bogoliubov, N.M. Malyshev, C. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T17:03:50Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148588 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:03:50Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bogoliubov, N.M. Malyshev, C. 2019-02-18T16:17:21Z 2019-02-18T16:17:21Z 2017 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 https://nasplib.isofts.kiev.ua/handle/123456789/148588 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. This work was supported by RFBR grant 16-01-00296. N.M.B. acknowledges the Simons Center
 for Geometry and Physics, Stony Brook University at which some of the research for this paper
 was performed. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Zero Range Process and Multi-Dimensional Random Walks Article published earlier |
| spellingShingle | Zero Range Process and Multi-Dimensional Random Walks Bogoliubov, N.M. Malyshev, C. |
| title | 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_short | Zero Range Process and Multi-Dimensional Random Walks |
| title_sort | zero range process and multi-dimensional random walks |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148588 |
| work_keys_str_mv | AT bogoliubovnm zerorangeprocessandmultidimensionalrandomwalks AT malyshevc zerorangeprocessandmultidimensionalrandomwalks |