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On the hyperplane conjecture for random convex sets

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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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Authors and Affiliations

  1. Department of Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Bo’az Klartag

  2. Department of Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel

    Gady Kozma

Authors
  1. Bo’az Klartag
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  2. Gady Kozma
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Correspondence to Bo’az Klartag.

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Supported by the Clay Mathematics Institute and by NSF grant #DMS-0456590

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Klartag, B., Kozma, G. On the hyperplane conjecture for random convex sets. Isr. J. Math. 170, 253–268 (2009). https://doi.org/10.1007/s11856-009-0028-7

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  • DOI: https://doi.org/10.1007/s11856-009-0028-7

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