Zero Range Process and Multi-Dimensional Random Walks

Abstract

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.

The boundary driven zero-range process

“…In this model, a particle leaves a site according to a jump rate g(k) that only depends on the number of particles, k, in that site. The zero-range process has been mostly studied in infinite lattices (see [2,3,18,19,26]) and in discrete torus (see [20,21,4,9,22] and the references therein). In the present work we consider the process defined in the finite lattice I N = {1, .…”

Correlation Functions as Nests of Self-Avoiding Paths

“…The aim of this paper is to represent correlation functions of XX0 spin chain as sums over nests of self-avoiding lattice paths. The interpretation of correlation functions of bosonic integrable models in terms of random walks in multidimensional simplectical lattices was given in [20,21].…”