Hierarchical models of interacting diffusions: Multiple time scale phenomena, phase transition and pattern of cluster-formation
The purpose of this paper is to explore the connection between multiple space-time scale behaviour for block averages and phase transitions, respectively formation of clusters, in infinite systems with locally interacting components. The essential object is the associated Markov chain which describes the joint distribution of the block averages at different time scales. A fixed-point and stability property of a particular dynamical system under a renormalisation procedure is used to explain this pattern of cluster formation and the fact that the long-time behaviour is universal in entire classes of evolutions.
scientific article; zbMATH DE number 568992