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Higher Order Concentration in Presence of Poincaré-Type Inequalities

  • Friedrich GötzeEmail author
  • Holger Sambale
Conference paper
Part of the Progress in Probability book series (PRPR, volume 74)

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.

Keywords

Concentration of measure phenomenon Poincaré inequalities 

1991 Mathematics Subject Classification

Primary 60E15 60F10; Secondary 60B20 

Notes

Acknowledgement

This research was supported by CRC 1283.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of MathematicsBielefeld UniversityBielefeldGermany

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