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arXiv · 1709.06838

Higher Order Concentration of Measure

Sergey G. Bobkov·Friedrich Götze·Holger Sambale
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Abstract

We study sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order $d-1$ for any $d \in \mathbb{N}$. The bounds are based on $d$-th 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).

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Sergey G. Bobkov, Friedrich Götze, Holger Sambale. 2017-09-20. Higher Order Concentration of Measure. https://doi.org/10.1142/s0219199718500438

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