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Search: MSC category 52A23 ( Asymptotic theory of convex bodies [See also 46B06] )

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1. CMB 2015 (vol 59 pp. 204)

Spektor, Susanna
 Restricted Khinchine Inequality We prove a Khintchine type inequality under the assumption that the sum of Rademacher random variables equals zero. We also show a new tail-bound for a hypergeometric random variable. Keywords:Khintchine inequality, Kahane inequality, Rademacher random variables, hypergeometric distribution.Categories:46B06, 60E15, 52A23, 46B09

2. CMB 2012 (vol 57 pp. 3)

Adamczak, Radosław; Latała, Rafał; Litvak, Alexander E.; Oleszkiewicz, Krzysztof; Pajor, Alain; Tomczak-Jaegermann, Nicole
 A Short Proof of Paouris' Inequality We give a short proof of a result of G.~Paouris on the tail behaviour of the Euclidean norm $|X|$ of an isotropic log-concave random vector $X\in\mathbb{R}^n,$ stating that for every $t\geq 1$, $\mathbb{P} \big( |X|\geq ct\sqrt n\big)\leq \exp(-t\sqrt n).$ More precisely we show that for any log-concave random vector $X$ and any $p\geq 1$, $(\mathbb{E}|X|^p)^{1/p}\sim \mathbb{E} |X|+\sup_{z\in S^{n-1}}(\mathbb{E} |\langle z,X\rangle|^p)^{1/p}.$ Keywords:log-concave random vectors, deviation inequalitiesCategories:46B06, 46B09, 52A23
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