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Higher Order Concentration in Presence of Poincaré-Type Inequalities

  • Friedrich GötzeEmail author
  • Holger Sambale
Conference paper
First Online:
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 
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Notes

Acknowledgement

This research was supported by CRC 1283.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of MathematicsBielefeld UniversityBielefeldGermany

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