Proceedings of the American Mathematical Society

Author(s): Guillaume Aubrun
Journal: Proc. Amer. Math. Soc. 135 (2007), 1293-1303.
MSC (2000): Primary 15A52, 52A20
Posted: November 14, 2006
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Abstract: We prove the following result: for any $\varepsilon >0$ , only $C(\varepsilon)n$ sample points are enough to obtain $(1+\varepsilon)$ -approximation of the inertia ellipsoid of an unconditional convex body in $\mathbf{R}^n$ . Moreover, for any $\rho >1$ , already $\rho n$ sample points give isomorphic approximation of the inertia ellipsoid. The proofs rely on an adaptation of the moments method from Random Matrix Theory.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 15A52, 52A20

Guillaume Aubrun
Affiliation: Institut de Mathématiques de Jussieu, Projet Analyse Fonctionnelle, Université de Paris 6, 175 rue du Chevaleret, 75013 Paris, France
Address at time of publication: Institut Camille Jordan, Université de Lyon 1, 21 Avenue Claude Bernard, 69622 Villeurbanne, Cedex France

DOI: 10.1090/S0002-9939-06-08615-1
PII: S 0002-9939(06)08615-1
Keywords: Isotropic, random matrix, convex body, moments method
Received by editor(s): December 1, 2005
Received by editor(s) in revised form: December 21, 2005
Posted: November 14, 2006
Additional Notes: This research was supported in part by the European Network PHD, FP6 Marie Curie Actions, MCRN-511953 and was done in part while the author was visiting the University of Athens.
Communicated by: N. Tomczak-Jaegermann
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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