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On the isotropy constant of random convex sets

Author: David Alonso-Gutiérrez
Journal: Proc. Amer. Math. Soc. 136 (2008), 3293-3300
MSC (2000): Primary 52A20
Published electronically: April 17, 2008
MathSciNet review: 2407095
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Abstract: Let $ K$ be the symmetric convex hull of $ m$ independent random vectors uniformly distributed on the unit sphere of $ \mathbb{R}^n$. We prove that, for every $ \delta>0$, the isotropy constant of $ K$ is bounded by a constant $ c(\delta)$ with high probability, provided that $ m\geq (1+\delta)n$.

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Additional Information

David Alonso-Gutiérrez
Affiliation: Institute of Mathematics, Universidad de Zaragoza, 50009 Zaragoza, Spain

Received by editor(s): July 10, 2007
Published electronically: April 17, 2008
Additional Notes: The author was supported by an FPU Scholarship from MEC (Spain), MCYT Grants (Spain) MTM2007-61446, DGA E-64 and by Marie Curie RTN CT-2004-511953
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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