Higher order concentration of measure

Sergey G. Bobkov, Friedrich Götze, Holger Sambale

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order d-1 for any d N. The bounds are based on dth order derivatives or difference operators. In particular, we consider deviations of functions of independent random variables and differentiable functions over probability measures satisfying a logarithmic Sobolev inequality, and functions on the unit sphere. Applications include concentration inequalities for U-statistics as well as for classes of symmetric functions via polynomial approximations on the sphere (Edgeworth-type expansions).

Original languageEnglish (US)
Article number1850043
JournalCommunications in Contemporary Mathematics
Volume21
Issue number3
DOIs
StatePublished - May 1 2019

Bibliographical note

Funding Information:
This research was supported by CRC 1283. The work of S. G. Bobkov was supported by NSF grant DMS-1612961 and by the Russian Academic Excellence Project ‘5-100’.

Publisher Copyright:
© 2019 World Scientific Publishing Company.

Keywords

  • Concentration of measure phenomenon
  • Efron-Stein inequality
  • Hoeffding decomposition
  • functions on the discrete cube
  • logarithmic Sobolev inequalities

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