SIGMA, 2017, Volume 13, 056, 14 pp.
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
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.
zero range process; conditional probability; multi-dimensional random walk; correlation function; symmetric functions.
|Russian Foundation for Basic Research
|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
PDF file (448 kB)
MSC: 05A19; 05E05; 82B23
Received: March 28, 2017; in final form July 14, 2017; Published online July 22, 2017
Nicolay M. Bogoliubov, Cyril Malyshev, “Zero Range Process and Multi-Dimensional Random Walks”, SIGMA, 13 (2017), 056, 14 pp.
Citation in format AMSBIB
\by Nicolay~M.~Bogoliubov, Cyril~Malyshev
\paper Zero Range Process and Multi-Dimensional Random Walks
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