Concentration of mass and central limit properties of isotropic convex bodies

Author:
G. Paouris

Journal:
Proc. Amer. Math. Soc. **133** (2005), 565-575

MSC (2000):
Primary 52A20; Secondary 52A38, 52A40

DOI:
https://doi.org/10.1090/S0002-9939-04-07757-3

Published electronically:
September 20, 2004

MathSciNet review:
2093081

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Abstract: We discuss the following question: Do there exist an absolute constant and a sequence tending to infinity with , such that for every isotropic convex body in and every the inequality holds true? Under the additional assumption that is 1-unconditional, Bobkov and Nazarov have proved that this is true with . The question is related to the central limit properties of isotropic convex bodies. Consider the spherical average . We prove that for every and every isotropic convex body in , the statements (A) ``for every , " and (B) ``for every , , where " are equivalent.

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Additional Information

**G. Paouris**

Affiliation:
Department of Mathematics, University of Crete, Iraklion 714-09, Greece

Email:
paouris@math.uoc.gr

DOI:
https://doi.org/10.1090/S0002-9939-04-07757-3

Keywords:
Isotropic convex bodies,
concentration of volume,
central limit theorem

Received by editor(s):
August 2, 2003

Published electronically:
September 20, 2004

Communicated by:
Nicole Tomczak-Jaegermann

Article copyright:
© Copyright 2004
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.