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Currently displaying 1 – 3 of 3

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Concentration of mass on the Schatten classes

O. Guédon; G. Paouris — 2007

Annales de l'I.H.P. Probabilités et statistiques

An isomorphic Dvoretzky's theorem for convex bodies

Y. Gordon; O. Guédon; M. Meyer — 1998

Studia Mathematica

We prove that there exist constants C>0 and 0 < λ < 1 so that for all convex bodies K in $ℝ^{n}$ with non-empty interior and all integers k so that 1 ≤ k ≤ λn/ln(n+1), there exists a k-dimensional affine subspace Y of $ℝ^{n}$ satisfying $d (Y \cap K, B_{2}^{k}) \leq C (1 + \sqrt (k / l n (n / (k l n (n + 1))))$ . This formulation of Dvoretzky’s theorem for large dimensional sections is a generalization with a new proof of the result due to Milman and Schechtman for centrally symmetric convex bodies. A sharper estimate holds for the n-dimensional simplex.

Majorizing measures and proportional subsets of bounded orthonormal systems..

O. Guédon; S. Mendelson; A. Pajor; N. Tomczak-Jaegermann — 2008

Revista Matemática Iberoamericana

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