A mixture of the exclusion process and the voter model

We consider a one-dimensional nearest-neighbour interacting particle system , which is a mixture of the simple exclusion process and the voter model. T he 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 n umber of empty sites to the left of it. We obtain criteria for the ergodici ty and some other properties of this system using the method of Lyapunov fu nctions.