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The subgaussian constant and concentration inequalities

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Abstract

We study concentration inequalities for Lipschitz functions on graphs by estimating the optimal constant in exponential moments of subgaussian type. This is illustrated on various graphs and related to various graph constants. We also settle, in the affirmative, a question of Talagrand on a deviation inequality for the discrete cube.

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Author information

Authors and Affiliations

  1. School of Mathematics, University of Minnesota, 55455, Minneapolis, MN, USA

    S. G. Bobkov

  2. Laboratoire d'Analyse et de Mathematiques Appliquées CNRS, UMR 8050, Université Paris XII, 94010, Créteil Cedex, France

    C. Houdré

  3. School of Mathematics, Georgia Institute of Technology, 30332-0170, Atlanta, GA, USA

    C. Houdré

  4. School of Mathematics and College of Computing, Georgia Institute of Technology, 30332-0160, Atlanta, GA, USA

    P. Tetali

Authors
  1. S. G. Bobkov
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  2. C. Houdré
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  3. P. Tetali
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Additional information

Research supported in part by NSF Grant No. DMS-0405587 and by EPSRC Visiting Fellowship.

Research supported in part by NSF Grant No. DMS-9803239, DMS-0100289.

Research supported in part by NSF Grant No. DMS-0401239.

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Bobkov, S.G., Houdré, C. & Tetali, P. The subgaussian constant and concentration inequalities. Isr. J. Math. 156, 255–283 (2006). https://doi.org/10.1007/BF02773835

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  • DOI: https://doi.org/10.1007/BF02773835

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