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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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