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We study variants of one-dimensional q-color voter models in discrete time.In addition to the usual voter model transitions in which a color is chosenfrom the left or right neighbor of a site there are two types of noisytransitions. One is bulk nucleation where a new random color is chosen. Theother is boundary nucleation where a random color is chosen only if the twoneighbors have distinct colors. We prove under a variety of conditions on q andthe magnitudes of the two noise parameters that the system is ergodic, i.e.,there is convergence to a unique invariant distribution. The methods arepercolation-based using the graphical structure of the model which consists ofcoalescing random walks combined with branching (boundary nucleation) and dying(bulk nucleation).

Ergodicity and Percolation for Variants of One-dimensional Voter Models