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Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces
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  • Published: 09 May 2006

Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces

  • François Bolley1 nAff2,
  • Arnaud Guillin2 &
  • Cédric Villani1 

Probability Theory and Related Fields volume 137, pages 541–593 (2007)Cite this article

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Abstract

We establish quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some error bounds for particle simulations in a model mean field problem. The tools include coupling arguments, as well as regularity and moment estimates for solutions of certain diffusive partial differential equations.

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Author information

Author notes
  1. François Bolley

    Present address: CEREMADE, Université Paris Dauphine, Paris, France

Authors and Affiliations

  1. ENS Lyon, Umpa, 46 allée d’Italie, F69364, Lyon Cedex 07, France

    François Bolley & Cédric Villani

  2. CEREMADE, Université Paris Dauphine, Paris, France

    Arnaud Guillin

Authors
  1. François Bolley
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  2. Arnaud Guillin
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  3. Cédric Villani
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Corresponding author

Correspondence to Cédric Villani.

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Cite this article

Bolley, F., Guillin, A. & Villani, C. Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces. Probab. Theory Relat. Fields 137, 541–593 (2007). https://doi.org/10.1007/s00440-006-0004-7

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  • Received: 26 April 2005

  • Revised: 22 February 2006

  • Published: 09 May 2006

  • Issue Date: March 2007

  • DOI: https://doi.org/10.1007/s00440-006-0004-7

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Keywords and phrases

  • Transport inequalities
  • Sanov Theorem
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