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 language | English (US) |
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Article number | 1850043 |
Journal | Communications in Contemporary Mathematics |
Volume | 21 |
Issue number | 3 |
DOIs | |
State | Published - May 1 2019 |
Externally published | Yes |
Bibliographical note
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