Duality for general attractive spin systems with applications in one dimension (Q1083138)

Duality has become an important tool in the theory of interacting spin systems in \({\mathbb{Z}}^ d\). In this paper a new version of dual processes is introduced, whose paths take their values in the collection of finite subsets instead of the elements of \({\mathbb{Z}}^ d\). They promise to be applicable to more general classes of processes than the previous ones, which were limited to special cases. As an example, the author generalizes results of \textit{R. Durrett} and \textit{D. Griffeath} [ibid. 11, 1-15 (1983; Zbl 0508.60080)], which they proved for the nearest neighbour one-dimensional contact process to all attractive nearest neighbour one-dimensional spin systems with critical behaviour. These results concern exponential convergence starting from all 1's to an equilibrium measure, which has exponentially decaying correlation functions.