About the isotropy constant of random convex sets

2007/07/11 by David Alonso-Gutierrez, Alonso-Gutierrez, David
Mathematics · #46B20 #52A20 #52A40 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #math.FA #math.MG #msc:46B20 #msc:52A20 #msc:52A40

paper · pdf · doi:10.48550/arxiv.0707.1570

8 pages

arxiv created 2007/07/11 · arxiv updated 2009/12/01

Abstract

Let K be the symmetric convex hull of m independent random vectors uniformly distributed on the unit sphere of Rⁿ. We prove that, for every δ>0, the isotropy constant of K is bounded by a constant c(δ) with high probability, provided that m≥ (1+δ)n.

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