Centroid Bodies and the Logarithmic Laplace Transform - A Unified Approach

2011/03/15 by Bo'az Klartag, Emanuel Milman, Klartag, Bo'az +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1103.2985

arxiv created 2011/03/15 · arxiv updated 2011/03/16

Abstract

We unify and slightly improve several bounds on the isotropic constant of high-dimensional convex bodies; in particular, a linear dependence on the body's psi-2 constant is obtained. Along the way, we present some new bounds on the volume of L_p-centroid bodies and yet another equivalent formulation of Bourgain's hyperplane conjecture. Our method is a combination of the L_p-centroid body technique of Paouris and the logarithmic Laplace transform technique of the first named author.

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