On the hyperplane conjecture for random convex sets

By Bo'az Klartag, Gady Kozma. 2006

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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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d99e43bd4acd63d1134464299a195deeac691136