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
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Summary: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