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arXiv 2012-05-11 DOI 10.4153/CMB-2012-014-5 0 views

A short proof of Paouris' inequality

Adamczak, Radosław · Latała, Rafał · Litvak, Alexander E. · Oleszkiewicz, Krzysztof · Pajor, Alain · Tomczak-Jaegermann, Nicole

Original · EN

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∈ⁿ, stating that for every t≥ 1, P(|X|≥ ct√ n)≤ (-t√ n). More precisely we show that for any log-concave random vector X and any p≥ 1, (E|X|ᵖ)¹/ᵖ E |X|+∈ ₛⁿ⁻¹(E |< z,X>|ᵖ)¹/ᵖ.

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