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On the hyperplane conjecture for random convex sets

^aDepartment of Mathematics, Princeton University, Princeton, NJ, 08544, USA
^bPrinceton University#TAB#
^cDepartment of Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel
^dWeizmann Institute of Science
✉Corresponding author

Israel Journal of Mathematics Hebrew University of Jerusalem2009-03-01 48 citations30 references

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Abstract

Let N ≥ n + 1, and denote by K the convex hull of N independent standard gaussian random vectors in ℝn. We prove that with high probability, the isotropic constant of K is bounded by a universal constant. Thus we verify the hyperplane conjecture for the class of gaussian random polytopes.

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On the hyperplane conjecture for random convex sets

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