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Concentration inequalities for random fields via coupling
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  • Published: 22 September 2006

Concentration inequalities for random fields via coupling

  • J. -R. Chazottes1,
  • P. Collet1,
  • C. Külske2 &
  • …
  • F. Redig3 

Probability Theory and Related Fields volume 137, pages 201–225 (2007)Cite this article

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  • 43 Citations

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Abstract

We present a new and simple approach to concentration inequalities in the context of dependent random processes and random fields. Our method is based on coupling and does not use information inequalities. In case one has a uniform control on the coupling, one obtains exponential concentration inequalities. If such a uniform control is no more possible, then one obtains polynomial or stretched-exponential concentration inequalities. Our abstract results apply to Gibbs random fields, both at high and low temperatures and in particular to the low-temperature Ising model which is a concrete example of non-uniformity of the coupling.

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Author information

Authors and Affiliations

  1. Centre de Physique Théorique, CNRS UMR 7644, 91128, Palaiseau Cedex, France

    J. -R. Chazottes & P. Collet

  2. Department of Mathematics and Computing Sciences, University of Groningen, Blauwborgje 3, 9747, AC, Groningen, The Netherlands

    C. Külske

  3. Mathematisch Instituut Universiteit Leiden, Niels Bohrweg 1, 2333, CA, Leiden, The Netherlands

    F. Redig

Authors
  1. J. -R. Chazottes
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  2. P. Collet
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  3. C. Külske
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  4. F. Redig
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Corresponding author

Correspondence to F. Redig.

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Chazottes, J.R., Collet, P., Külske, C. et al. Concentration inequalities for random fields via coupling. Probab. Theory Relat. Fields 137, 201–225 (2007). https://doi.org/10.1007/s00440-006-0026-1

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  • Received: 28 March 2005

  • Revised: 28 June 2006

  • Published: 22 September 2006

  • Issue Date: January 2007

  • DOI: https://doi.org/10.1007/s00440-006-0026-1

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Keywords

  • Exponential concentration
  • Stretched-exponential concentration
  • Moment inequality
  • Gibbs random fields
  • Ising model
  • Orlicz space
  • Luxembourg norm
  • Kantorovich–Rubinstein theorem

Mathematical Subject Classification (2000)

  • 60k35 (Primary)
  • 82c22 (Secondary)
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