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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The covering numbers and ``low $M^*$-estimate"
for quasi-convex bodies


Authors: A. E. Litvak, V. D. Milman and A. Pajor
Journal: Proc. Amer. Math. Soc. 127 (1999), 1499-1507
MSC (1991): Primary 52C17; Secondary 46B07, 52A21, 52A30
Published electronically: January 29, 1999
MathSciNet review: 1469422
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Abstract | References | Similar Articles | Additional Information

Abstract: This article gives estimates on the covering numbers and diameters of random proportional sections and projections of quasi-convex bodies in $\mathbb{R}^n$. These results were known for the convex case and played an essential role in the development of the theory. Because duality relations cannot be applied in the quasi-convex setting, new ingredients were introduced that give new understanding for the convex case as well.


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Additional Information

A. E. Litvak
Affiliation: Department of Mathematics, Tel Aviv University, Ramat Aviv, Israel
Address at time of publication: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: alexandr@math.tau.ac.il, alexandr@math.ualberta.ca

V. D. Milman
Email: vitali@math.tau.ac.il

A. Pajor
Affiliation: Universite de Marne-la-Valle, Equipe de Mathematiques, 2 rue de la Butte Verte, 93166, Noisy-le-Grand Cedex, France
Email: pajor@math.univ-mlv.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04593-1
PII: S 0002-9939(99)04593-1
Received by editor(s): September 19, 1996
Received by editor(s) in revised form: June 14, 1997
Published electronically: January 29, 1999
Additional Notes: This research was done while the authors visited MSRI; we thank the Institute for its hospitality.
The first and second authors research was partially supported by BSF
Communicated by: Dale E. Alspach
Article copyright: © Copyright 1999 American Mathematical Society