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Concentration of mass on convex bodies

Abstract : 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}) <= exp (-root nt) for every t >= 1, where L-K denotes the isotropic constant.
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Submitted on : Wednesday, May 2, 2012 - 11:38:27 PM
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G. Paouris. Concentration of mass on convex bodies. Geometric And Functional Analysis, Springer Verlag, 2006, 16 (5), pp.1021--1049. ⟨10.1007/s00039-006-0584-5⟩. ⟨hal-00693783⟩



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