On the isotropy constant of random convex sets

Alonso-Gutiérrez, David

doi:10.1090/S0002-9939-08-09487-2

On the isotropy constant of random convex sets
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by David Alonso-Gutiérrez

Proc. Amer. Math. Soc. 136 (2008), 3293-3300

DOI: https://doi.org/10.1090/S0002-9939-08-09487-2

Published electronically: April 17, 2008

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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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