On Multiplier Processes Under Weak Moment Assumptions

  • Shahar Mendelson
Part of the Lecture Notes in Mathematics book series (LNM, volume 2169)


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 \(\|\big< X,t\big >\| _{L_{p}} \leq L\sqrt{p}\) for every t ∈ Sn−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.


Random Vector Linear Functional Independent Copy Isotropic Vector Bernoulli Process 
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S. Mendelson is supported in part by the Israel Science Foundation.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsTechnion - I.I.T.HaifaIsrael
  2. 2.Mathematical Sciences InstituteThe Australian National UniversityCanberraAustralia

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