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On random intersections of two convex bodies. Appendix to: "Isoperimetry of waists and local versus global asymptotic convex geometries" by R.Vershynin

Mark Rudelson·Roman Vershynin
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Abstract

In the paper "Isoperimetry of waists and local versus global asymptotic convex geometries", it was proved that the existence of nicely bounded sections of two symmetric convex bodies K and L implies that the intersection of randomly rotated K and L is nicely bounded. In this appendix, we achieve a polynomial bound on the diameter of that intersection (in the ratio of the dimensions of the sections).

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Mark Rudelson, Roman Vershynin. 2004-04-27. On random intersections of two convex bodies. Appendix to: "Isoperimetry of waists and local versus global asymptotic convex geometries" by R.Vershynin. https://arxiv.org/abs/math/0404502

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