# [Banach] Abstract of a paper by Emanuel Milman

Dale Alspach alspach at www.math.okstate.edu
Fri Apr 28 08:25:05 CDT 2006

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 at weizmann.ac.il

The paper may be downloaded from the archive by web browser from
URL

http://front.math.ucdavis.edu/math.FA/0604595

or

http://arXiv.org/abs/math.FA/0604595

or by email in unzipped form by transmitting an empty message with
subject line

uget 0604595

or in gzipped form by using subject line

get 0604595

to: math at arXiv.org.