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A large deviation approach to some transportation cost inequalities
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  • Published: 12 December 2006

A large deviation approach to some transportation cost inequalities

  • Nathael Gozlan1 &
  • Christian Léonard1,2 

Probability Theory and Related Fields volume 139, pages 235–283 (2007)Cite this article

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Abstract

New transportation cost inequalities are derived by means of elementary large deviation reasonings. Their dual characterization is proved; this provides an extension of a well-known result of S. Bobkov and F. Götze. Their tensorization properties are investigated. Sufficient conditions (and necessary conditions too) for these inequalities are stated in terms of the integrability of the reference measure. Applying these results leads to new deviation results: concentration of measure and deviations of empirical processes.

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Author information

Authors and Affiliations

  1. Modal-X, Université Paris 10, Bât. G, 200 av. de la République, 92001, Nanterre Cedex, France

    Nathael Gozlan & Christian Léonard

  2. CMAP, École Polytechnique, 91128, Palaiseau Cedex, France

    Christian Léonard

Authors
  1. Nathael Gozlan
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  2. Christian Léonard
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Correspondence to Christian Léonard.

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Cite this article

Gozlan, N., Léonard, C. A large deviation approach to some transportation cost inequalities. Probab. Theory Relat. Fields 139, 235–283 (2007). https://doi.org/10.1007/s00440-006-0045-y

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  • Received: 18 July 2005

  • Revised: 06 November 2006

  • Published: 12 December 2006

  • Issue Date: September 2007

  • DOI: https://doi.org/10.1007/s00440-006-0045-y

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Keywords

  • Transportation cost inequalities
  • Large deviations
  • Concentration of measure

Mathematics Subject Classification (2000)

  • 60E15
  • 60F10
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