Concentration of mass on convex bodies

Concentration of mass on convex bodies

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 R-n, then Prob ({x is an element of K : parallel to x parallel to(2) >= c root nL(K)t}) = 1, where L-K denotes the isotropic co...

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Veröffentlicht in:Geometric and functional analysis 2006-12, Vol.16 (5), p.1021-1049
1. Verfasser: Paouris, G.
Format: Artikel
Sprache:eng
Schlagworte:
Mathematical Physics
Mathematics
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Zusammenfassung: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 R-n, then Prob ({x is an element of K : parallel to x parallel to(2) >= c root nL(K)t}) = 1, where L-K denotes the isotropic constant.
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-006-0584-5