Zero Range Process and Multi-Dimensional Random Walks

Symmetry Integrability and Geometry-Methods and Applications

article

Nicolay M. Bogoliubov¹  Cyril Malyshev¹ 

[1] ITMO University

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

DOI  :  10.3842/SIGMA.2017.056

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown