Invariant measures for the multitype voter model (Q808114)

The multitype voter model is investigated. This model is described as follows. Let S be a countable set and p(x,y) the transition probability for an irreducible Markov chain on S. S is regarded as a collection of voters, each having one of countably many possible positions denoted by \(\{\) 0,1,2,...\(\}\) on an issue. Each voter x waits an exponential time with parameter one and then, he chooses a voter y with probability p(x,y) and adopts the position of y. A Markov process describing the time evolution of this model is constructed on \(\{0,1,2,...\}^ S\). Moreover all extremal invariant measures for this model are found and the domain of attraction of each of them is determined.