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

Liu, Xijian

Ann. Probab. 23, No. 3, 1439-1455 (1995).

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

Keywords:

exclusion process; voter model; coalescing random walk; duality; ergodic theorem