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Time dependent critical fluctuations of a one dimensional local mean field model
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  • Published: September 1995

Time dependent critical fluctuations of a one dimensional local mean field model

  • J. Fritz1 &
  • B. Rüdiger2 

Probability Theory and Related Fields volume 103, pages 381–407 (1995)Cite this article

  • 154 Accesses

  • 12 Citations

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Summary

One-dimensional stochastic Ising systems with a local mean field interaction (Kac potential) are investigated. It is shown that near the critical temperature of the equilibrium (Gibbs) distribution the time dependent process admits a scaling limit given by a nonlinear stochastic PDE. The initial conditions of this approximation theorem are then verified for equilibrium states when the temperature goes to its critical value in a suitable way. Earlier results of Bertini-Presutti-Rüdiger-Saada are improved, the proof is based on an energy inequality obtained by coupling the Glauber dynamics to its voter type, linear approximation.

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Author information

Authors and Affiliations

  1. Department of Probability and Statistics, Eötvös Lóránd University of Sciences, Múzeum Krt. 6-8, H-1088, Budapest, Hungary

    J. Fritz

  2. Dipartimento di Matematica, Universitá di Roma II, Tor Vergata, Via della Ricerca Scientifica, I-00133, Roma, Italy

    B. Rüdiger

Authors
  1. J. Fritz
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  2. B. Rüdiger
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Fritz, J., Rüdiger, B. Time dependent critical fluctuations of a one dimensional local mean field model. Probab. Th. Rel. Fields 103, 381–407 (1995). https://doi.org/10.1007/BF01195480

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  • Received: 02 December 1994

  • Revised: 20 April 1995

  • Issue Date: September 1995

  • DOI: https://doi.org/10.1007/BF01195480

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Mathematics Subject Classification (1991)

  • 60K35
  • 82A05
  • 82B40
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