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
Date:2017
Main Authors: Bogoliubov, N.M., Malyshev, C.
Format: Article
Language:English
Published: Інститут математики НАН України 2017
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
id nasplib_isofts_kiev_ua-123456789-148588
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Zero Range Process and Multi-Dimensional Random Walks
spellingShingle Zero Range Process and Multi-Dimensional Random Walks
Bogoliubov, N.M.
Malyshev, C.
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
author Bogoliubov, N.M.
Malyshev, C.
author_facet Bogoliubov, N.M.
Malyshev, C.
publishDate 2017
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.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.
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first_indexed 2025-12-07T17:03:50Z
last_indexed 2025-12-07T17:03:50Z
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