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Hierarchical models of interacting diffusions: Multiple time scale phenomena, phase transition and pattern of cluster-formation
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  • Published: December 1993

Hierarchical models of interacting diffusions: Multiple time scale phenomena, phase transition and pattern of cluster-formation

  • Donald A. Dawson1 &
  • Andreas Greven2 

Probability Theory and Related Fields volume 96, pages 435–473 (1993)Cite this article

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  • 32 Citations

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Summary

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 longtime behaviour is universal in entire classes of evolutions.

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Authors and Affiliations

  1. Department of Mathematics, Carleton University, K1S 5B6, Ottawa, Canada

    Donald A. Dawson

  2. Institut für Mathematische Stochastik, Lotzestrasse 13, D-37083, Göttingen, Germany

    Andreas Greven

Authors
  1. Donald A. Dawson
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  2. Andreas Greven
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Dawson, D.A., Greven, A. Hierarchical models of interacting diffusions: Multiple time scale phenomena, phase transition and pattern of cluster-formation. Probab. Th. Rel. Fields 96, 435–473 (1993). https://doi.org/10.1007/BF01200205

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  • Received: 28 October 1991

  • Revised: 04 March 1993

  • Issue Date: December 1993

  • DOI: https://doi.org/10.1007/BF01200205

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Mathematics Subject Classification (1991)

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