A limit theorem for a class of interacting particle systems (Q1897177)

Let \(S\) be a countable set and \(\Lambda\) the collection of all subsets of \(S\). We consider interacting particle systems (IPS) \(\{\eta_t\}\) on \(\Lambda\), with duals \(\{\widetilde {\eta}_t\}\) and duality equation \(P [|\eta^\zeta_t \cap A|\text{ odd}]= \widetilde {P} [|\widetilde{\eta}^A_t \cap \zeta |\text{ odd}]\), \(\zeta, A \subset S\), \(A\) finite. Under certain conditions we find all the extreme invariant distributions that arise as limits of translation invariant initial configurations. Specific systems will be considered. A new property of the annihilating particle model is then used to prove a limiting relation between the annihilating and coalescing particle models.