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Higher order concentration in presence of Poincaré-type inequalities. (English) Zbl 1443.60024

Gozlan, Nathael (ed.) et al., High dimensional probability VIII. The Oaxaca volume. Selected papers based on the presentations at the 8th conference on high-dimensional probability, HDP VIII, Casa Matemática Oaxaca (CMO), Mexico, May 28 – June 2, 2017. Cham: Birkhäuser. Prog. Probab. 74, 55-69 (2019).
Summary: 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.
For the entire collection see [Zbl 1431.60003].

MSC:

60E15 Inequalities; stochastic orderings
60F10 Large deviations
60B20 Random matrices (probabilistic aspects)
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