This is an announcement for the paper "About the isotropy constant of random convex sets" by David Alonso-Gutierrez.

Abstract: Let $K$ be the symmetric convex hull of $m$ independent random vectors uniformly distributed on the unit sphere of $\R^n$. We prove that, for every $\delta>0$, the isotropy constant of $K$ is bounded by a constant $c(\delta)$ with high probability, provided that $m\geq (1+\delta)n$.

Archive classification: math.FA

Mathematics Subject Classification: 52A20; 52A40; 46B20;

Remarks: 8 pages

The source file(s), Randomconvexsets8.tex: 18946 bytes, is(are) stored in gzipped form as 0707.1570.gz with size 6kb. The corresponding postcript file has gzipped size 72kb.

Submitted from: 498220@celes.unizar.es

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