Hierarchical models of interacting diffusions: Multiple time scale phenomena, phase transition and pattern of cluster-formation
type: Item
instance of: scholarly article
title: Hierarchical models of interacting diffusions: Multiple time scale phenomena, phase transition and pattern of cluster-formation
zbMATH Open document ID: 0794.60101
DOI: 10.1007/BF01200205
author: Donald A. Dawson
author: Andreas Greven
publication date: 1994-08-28T00:00:00Z
review text: 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.
reviewed by: Donald A. Dawson
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 568992
zbMATH Keywords: space-time scale behaviour
zbMATH Keywords: locally interacting components
zbMATH Keywords: fixed-point
zbMATH Keywords: stability property
zbMATH Keywords: dynamical system
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01200205
OpenAlex ID: W1974508794
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 568992