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Slow decay of Gibbs measures with heavy tails
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  • Published: 16 June 2009

Slow decay of Gibbs measures with heavy tails

  • Cyril Roberto1 

Probability Theory and Related Fields volume 148, pages 247–268 (2010)Cite this article

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Abstract

We consider Glauber dynamics reversible with respect to Gibbs measures with heavy tails in the case when spins are unbounded. The interactions are bounded and of finite range. The self-potential enters into two classes of measures, κ-concave probability measures and sub-exponential laws, for which it is known that no exponential decay can occur. Using coercive inequalities we prove that, for κ-concave probability measures, the associated infinite volume semi-group decays to equilibrium polynomially and stretched exponentially for sub-exponential laws. This improves and extends previous results by Bobkov and Zegarlinski.

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Authors and Affiliations

  1. Laboratoire d’Analyse et de Mathématiques Appliquées, UMR 8050, Université Française, Cité Descartes, 5 bd Descartes, 77454, Marne la vallée cedex 2, France

    Cyril Roberto

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  1. Cyril Roberto
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Corresponding author

Correspondence to Cyril Roberto.

Additional information

This work was supported by the European Research Council through the “Advanced Grant” PTRELSS 228032 and by GDRE 224 GREFI-MEFI, CNRS-INdAM.

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Cite this article

Roberto, C. Slow decay of Gibbs measures with heavy tails. Probab. Theory Relat. Fields 148, 247–268 (2010). https://doi.org/10.1007/s00440-009-0229-3

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  • Received: 30 October 2008

  • Revised: 01 May 2009

  • Published: 16 June 2009

  • Issue Date: September 2010

  • DOI: https://doi.org/10.1007/s00440-009-0229-3

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Keywords

  • Weak Poincaré inequality
  • Gibbs measures
  • Glauber dynamics
  • Unbounded spin systems
  • Heavy tails distributions

Mathematics Subject Classification (2000)

  • 60K35
  • 82C22
  • 26D10
  • 47D07
  • 82C20
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