This is an announcement for the paper "On Gaussian marginals of uniformly convex bodies" by Emanuel Milman.

Abstract: We show that many uniformly convex bodies have Gaussian marginals in most directions in a strong sense, which takes into account the tails of the distributions. These include uniformly convex bodies with power type 2, and power type p>2 with some additional type condition. In particular, all unit-balls of subspaces of L_p for 1<p<\infty have Gaussian marginals in this strong sense. Using the weaker Kolmogorov metric, we can extend our results to arbitrary uniformly convex bodies with power type p, for 2<=p<4. These results are obtained by putting the bodies in (surprisingly) non-isotropic positions and by a new concentration of volume observation for uniformly convex bodies.

Archive classification: Functional Analysis; Metric Geometry; Probability

Remarks: 21 pages

The source file(s), Gaussian-Marginals.bbl: 5089 bytes, Gaussian-Marginals.tex: 76495 bytes, is(are) stored in gzipped form as 0604595.tar.gz with size 24kb. The corresponding postcript file has gzipped size 93kb.

Submitted from: emanuel.milman@weizmann.ac.il

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