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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
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
Аннотация:
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.
Ключевые слова:
zero range process; conditional probability; multi-dimensional random walk; correlation function; symmetric functions.
Поступила: 28 марта 2017 г.; в окончательном варианте 14 июля 2017 г.; опубликована 22 июля 2017 г.
Образец цитирования:
Nicolay M. Bogoliubov, Cyril Malyshev, “Zero Range Process and Multi-Dimensional Random Walks”, SIGMA, 13 (2017), 056, 14 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1256 https://www.mathnet.ru/rus/sigma/v13/p56
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