On Gaussian Marginals of Uniformly Convex Bodies

Details On Gaussian Marginals of Uniformly Convex Bodies On Gaussian Marginals of Uniformly Convex Bodies

2006-04-27

arxiv.org/abs/math/0604595v3

Mathematics

Functional Analysis

21 pages, revised version comparing between our results and Klartag's, accepted for publication in Journal of Theoretical Prob

Scientific paper

Recently, Bo'az Klartag showed that arbitrary convex bodies have Gaussian marginals in most directions. We show that Klartag's quantitative estimates may be improved for many uniformly convex bodies. These include uniformly convex bodies with power type 2, and power type $p>2$ with some additional type condition. In particular, our results apply to all unit-balls of subspaces of quotients of $L_p$ for $1

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