Construction of the factorized steady state distribution in models of mass transport

TL;DR

This paper introduces a straightforward test for determining when certain one-dimensional mass transport models have factorized steady states, providing explicit construction methods and applying them to known and new models.

Contribution

It offers a simple test for factorization of steady states in mass transport models and constructs new models with factorized steady states.

Findings

Recovered known results for Zero-range and Asymmetric random average processes

Developed explicit construction method for single-site weights

Created new models with factorized steady states

Abstract

For a class of one-dimensional mass transport models we present a simple and direct test on the chipping functions, which define the probabilities for mass to be transferred to neighbouring sites, to determine whether the stationary distribution is factorized. In cases where the answer is affirmative, we provide an explicit method for constructing the single-site weight function. As an illustration of the power of this approach, previously known results on the Zero-range process and Asymmetric random average process are recovered in a few lines. We also construct new models, namely a generalized Zero-range process and a binomial chipping model, which have factorized steady states.