Götze, Friedrich; Sambale, Holger 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]. Cited in 1 Document MSC: 60E15 Inequalities; stochastic orderings 60F10 Large deviations 60B20 Random matrices (probabilistic aspects) Keywords:concentration of measure phenomenon; Poincaré inequalities PDFBibTeX XMLCite \textit{F. Götze} and \textit{H. Sambale}, Prog. Probab. 74, 55--69 (2019; Zbl 1443.60024) Full Text: DOI arXiv