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Götze, Friedrich; Sambale, Holger

Second order concentration via logarithmic Sobolev inequalities. (English) Zbl 1448.60049

Bernoulli 26, No. 1, 93-126 (2020).
The authors derive second-order concentration-of-measure results, that is, employing second-order difference (or differential) operators, and where fluctuations of random variables of the form \(f-\mathbb{E}f-f_1\) are considered, where \(f_1\) is the first-order term in the Hoeffding decomposition of \(f\). Both the differentiable and non-differentiable settings are studied. Proofs are based on modified logarithmic Sobolev inequalities and exponential inequalities. Applications are given to functions of independent random variables and in random matrix theory.
Reviewer: Fraser Daly (Edinburgh)

Cited in 3 Documents

MSC:

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

Keywords:

bootstrap approximation; concentration of measure phenomenon; functions on the discrete cube; Hoeffding decomposition; logarithmic Sobolev inequalities
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\textit{F. Götze} and \textit{H. Sambale}, Bernoulli 26, No. 1, 93--126 (2020; Zbl 1448.60049)
Full Text: DOI arXiv Euclid

References:

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