Concentration of mass on convex bodies

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• 作者：G. Paouris
• 关键词：Isotropic convex bodies ; concentration of volume ; tail estimates for linear functionals ; Lq ; centroid bodies
• 刊名：Geometric And Functional Analysis
• 出版年：2006
• 出版时间：December, 2006
• 年：2006
• 卷：16
• 期：5
• 页码：1021-1049
• 全文大小：378 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8970

文摘

We establish sharp concentration of mass inequality for isotropic convex bodies: there exists an absolute constant c > 0 such that if K is an isotropic convex body in \mathbbRn\mathbb{R}^{n} , then \textProb( { x ? K:||x||₂ \geqslant c?nL_K t } ) \leqslant exp( - ?nt ) {\text{Prob}}{\left( {{\left\{ {x \in K:||x||_{2} \geqslant c{\sqrt{n}}L_{K} t} \right\}}} \right)} \leqslant \exp {\left( { - {\sqrt{n}}t} \right)}