Inhomogeneous generalization of multispecies totally asymmetric zero range process

TL;DR

This paper introduces an inhomogeneous generalization of the multispecies totally asymmetric zero range process, providing a matrix product solution for the steady state and an algorithm based on combinatorial R.

Contribution

It extends the $n$-species TAZRP by incorporating inhomogeneous transition rates and derives the steady state in a novel matrix product form and combinatorial R-based algorithm.

Findings

Steady state probability expressed in matrix product form

Development of an algorithm using combinatorial R

Inhomogeneous transition rates incorporated into the model

Abstract

The $n$-species totally asymmetric zero range process ($n$-TAZRP) on one-dimensional periodic chain studied recently by the authors is a continuous time Markov process where arbitrary number of particles can occupy the same sites and hop to the adjacent sites only in one direction with a priority constraint according to their species. In this paper we introduce an $n$-parameter generalization of the $n$-TAZRP having inhomogeneous transition rate. The steady state probability is obtained in a matrix product form and also by an algorithm related to combinatorial $R$.