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The covering numbers and ``low  -estimate" for quasi-convex bodies
Author(s):
A.
E.
Litvak;
V.
D.
Milman;
A.
Pajor
Journal:
Proc. Amer. Math. Soc.
127
(1999),
1499-1507.
MSC (1991):
Primary 52C17;
Secondary 46B07, 52A21, 52A30
Posted:
January 29, 1999
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Abstract:
This article gives estimates on the covering numbers and diameters of random proportional sections and projections of quasi-convex bodies in  . 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
Affiliation:
Department of Mathematics, Tel Aviv University, Ramat Aviv, Israel
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:
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
Posted:
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
Copyright of article:
Copyright
1999,
American Mathematical Society
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