About the isotropy constant of random convex sets

Details About the isotropy constant of random convex sets About the isotropy constant of random convex sets

2007-07-11

arxiv.org/abs/0707.1570v1

Mathematics

Metric Geometry

8 pages

Scientific paper

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 $m\geq (1+\delta)n$.

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