A Mixture of the Exclusion Process and the Voter Model

TL;DR

This paper studies a one-dimensional interacting particle system combining the exclusion process and voter model, providing criteria for ergodicity and other properties using Lyapunov functions.

Contribution

It introduces a new mixed model of exclusion and voter dynamics and establishes conditions for its ergodic behavior.

Findings

Criteria for ergodicity of the mixed process

Conditions for system stability and recurrence

Application of Lyapunov functions to analyze particle systems

Abstract

We consider a one-dimensional nearest-neighbor interacting particle system, which is a mixture of the simple exclusion process and the voter model. The state space is taken to be the countable set of the configurations that have a finite number of particles to the right of the origin and a finite number of empty sites to the left of it. We obtain criteria for the ergodicity and some other properties of this system using the method of Lyapunov functions.