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SIGMA, 2017, Volume 13, 056, 14 pp. (Mi sigma1256)  

This article is cited in 1 scientific paper (total in 1 paper)

Zero Range Process and Multi-Dimensional Random Walks

Nicolay M. Bogoliubovab, Cyril Malyshevab

a St.-Petersburg Department of Steklov Institute of Mathematics of RAS, Fontanka 27, St.-Petersburg, Russia
b ITMO University, Kronverksky 49, St.-Petersburg, Russia

Abstract: 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.

Keywords: zero range process; conditional probability; multi-dimensional random walk; correlation function; symmetric functions.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00296_
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.


DOI: https://doi.org/10.3842/SIGMA.2017.056

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Bibliographic databases:

MSC: 05A19; 05E05; 82B23
Received: March 28, 2017; in final form July 14, 2017; Published online July 22, 2017
Language:

Citation: Nicolay M. Bogoliubov, Cyril Malyshev, “Zero Range Process and Multi-Dimensional Random Walks”, SIGMA, 13 (2017), 056, 14 pp.

Citation in format AMSBIB
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\by Nicolay~M.~Bogoliubov, Cyril~Malyshev
\paper Zero Range Process and Multi-Dimensional Random Walks
\jour SIGMA
\yr 2017
\vol 13
\papernumber 056
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\crossref{https://doi.org/10.3842/SIGMA.2017.056}
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    This publication is cited in the following articles:
    1. J. Math. Sci. (N. Y.), 238:6 (2019), 779–792  mathnet  crossref
  • Symmetry, Integrability and Geometry: Methods and Applications
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