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Higher Order Concentration in Presence of Poincaré-Type Inequalities

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High Dimensional Probability VIII

Part of the book series: Progress in Probability ((PRPR,volume 74))

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Abstract

We show sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order d − 1 for any \(d \in \mathbb {N}\). Here we focus on differentiable functions on the Euclidean space in presence of a Poincaré-type inequality. The bounds are based on d-th order derivatives.

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Acknowledgement

This research was supported by CRC 1283.

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Authors and Affiliations

  1. Faculty of Mathematics, Bielefeld University, Bielefeld, Germany

    Friedrich Götze & Holger Sambale

Authors
  1. Friedrich Götze
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  2. Holger Sambale
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Corresponding author

Correspondence to Friedrich Götze .

Editor information

Editors and Affiliations

  1. MAP 5, Université Paris Descartes, Paris, France

    Nathael Gozlan

  2. Institute of Mathematics, University of Warsaw, Warsaw, Poland

    Rafał Latała

  3. Centre de Mathématiques Appliquées, Ecole Polytechnique, Palaiseau, France

    Karim Lounici

  4. Department of Mathematical Sciences, University of Delaware, Newark, DE, USA

    Mokshay Madiman

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Götze, F., Sambale, H. (2019). Higher Order Concentration in Presence of Poincaré-Type Inequalities. In: Gozlan, N., Latała, R., Lounici, K., Madiman, M. (eds) High Dimensional Probability VIII. Progress in Probability, vol 74. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-26391-1_6

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