The covering numbers and “low $M^*$-estimate" for quasi-convex bodies
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- by A. E. Litvak, V. D. Milman and A. Pajor PDF
- Proc. Amer. Math. Soc. 127 (1999), 1499-1507 Request permission
Abstract:
This article gives estimates on the covering numbers and diameters of random proportional sections and projections of quasi-convex bodies in $\mathbb {R}$. 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.References
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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
- MR Author ID: 367520
- Email: alexandr@math.tau.ac.il, alexandr@math.ualberta.ca
- V. D. Milman
- MR Author ID: 125020
- ORCID: 0000-0003-4632-5487
- 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
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1499-1507
- MSC (1991): Primary 52C17; Secondary 46B07, 52A21, 52A30
- DOI: https://doi.org/10.1090/S0002-9939-99-04593-1
- MathSciNet review: 1469422