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Finite and infinite systems of interacting diffusions
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  • Published: June 1995

Finite and infinite systems of interacting diffusions

  • J. T. Cox1,
  • Andreas Greven2 &
  • Tokuzo Shiga3 

Probability Theory and Related Fields volume 103, pages 165–197 (1995)Cite this article

  • 215 Accesses

  • 19 Citations

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Summary

We study the problem of relating the long time behavior of finite and infinite systems of locally interacting components. We consider in detail a class of lincarly interacting diffusionsx(t)={x i (t),i ∈ ℤd} in the regime where there is a one-parameter family of nontrivial invariant measures. For these systems there are naturally defined corresponding finite systems,\(x^N (t) = \left\{ {x_i^N (t),i \in \Lambda _N } \right\}\), with\(\Lambda _N = ( - N,N]^d \cap \mathbb{Z}^d\). Our main result gives a comparison between the laws ofx(t N ) andx N(t N ) for timest N →∞ asN→∞. The comparison involves certain mixtures of the invariant measures for the infinite system.

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Author information

Authors and Affiliations

  1. Mathematics Department, Syracuse University, 13244, Syracuse, New York, USA

    J. T. Cox

  2. Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarekstrasse 1 1/2, D-91054, Erlangen, Germany

    Andreas Greven

  3. Department of Applied Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, 152, Tokyo, Japan

    Tokuzo Shiga

Authors
  1. J. T. Cox
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  2. Andreas Greven
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  3. Tokuzo Shiga
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Additional information

Partly supported by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University, by the National Science Foundation, and by the National Security Agency

Research supported in part by the DFG

Partly supported by S.R.63540155 of Japan Ministry of Education

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Cox, J.T., Greven, A. & Shiga, T. Finite and infinite systems of interacting diffusions. Probab. Th. Rel. Fields 103, 165–197 (1995). https://doi.org/10.1007/BF01204213

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  • Received: 20 December 1993

  • Revised: 15 December 1994

  • Issue Date: June 1995

  • DOI: https://doi.org/10.1007/BF01204213

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Mathematics Subject Classification (1991)

  • 60K35
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