## Symmetric two-particle exclusion-eating processes.(English)Zbl 0926.60088

Summary: We consider infinite particle systems on a countable set $$S$$ with two-particle exclusion-eating motion determined by a symmetric transition function $$p(x,y)$$. This is, in a certain sense, a mixture of the exclusion process and the voter model. We discuss the dual process of this process and use the dual process to give a description of the set of invariant measures and to prove an ergodic theorem.

### MSC:

 60K35 Interacting random processes; statistical mechanics type models; percolation theory
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