Product Measure Steady States of Generalized Zero Range Processes

TL;DR

This paper characterizes the conditions under which generalized zero range processes and related mass transport processes have factorizable steady states, extending understanding of their long-term behavior and state distributions.

Contribution

It provides necessary and sufficient conditions for the existence of factorizable steady states in generalized zero range processes and conjectures similar conditions for mass transport processes.

Findings

Established conditions for factorizable steady states in generalized zero range processes.

Proved sufficiency of conditions for continuous mass transport processes.

Conjectured necessity of these conditions for mass transport processes.

Abstract

We establish necessary and sufficient conditions for the existence of factorizable steady states of the Generalized Zero Range Process. This process allows transitions from a site $i$ to a site $i+q$ involving multiple particles with rates depending on the content of the site $i$, the direction $q$ of movement, and the number of particles moving. We also show the sufficiency of a similar condition for the continuous time Mass Transport Process, where the mass at each site and the amount transferred in each transition are continuous variables; we conjecture that this is also a necessary condition.