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On multiplier processes under weak moment assumptions. (English) Zbl 1366.60044
Klartag, Bo’az (ed.) et al., Geometric aspects of functional analysis. Israel seminar (GAFA) 2014–2016. Cham: Springer (ISBN 978-3-319-45281-4/pbk; 978-3-319-45282-1/ebook). Lecture Notes in Mathematics 2169, 301-318 (2017).
Summary: We show that if \(V \subset \mathbb{R}^{n}\) satisfies a certain symmetry condition that is closely related to unconditionality, and if \(X\) is an isotropic random vector for which \(\|\langle X, t\rangle\| _{L_{p}} \leq L\sqrt{p}\) for every \(t\in S^{n-1}\) and every \(1 \leq p\lesssim \log n\), then the suprema of the corresponding empirical and multiplier processes indexed by \(V\) behave as if \(X\) were \(L\)-subgaussian.
For the entire collection see [Zbl 1369.46001].

MSC:
60E05 Probability distributions: general theory
60G99 Stochastic processes
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