Threshold phenomena for high-dimensional random polytopes

2018/02/28 by Gilles Bonnet, Giorgos Chasapis, Julian Grote +2 · 1 voice
Mathematics · #Geometry and complex manifolds #Point processes and geometric inequalities #Random Matrices and Applications

paper · doi:10.1142/s0219199718500384

openalex created_date 2018/02/23 · openalex publication_date 2018/05/11 · openalex updated_date 2026/08/01

Abstract

Let [Formula: see text], [Formula: see text] be independent random points in [Formula: see text], distributed according to the so-called beta or beta-prime distribution, respectively. We establish threshold phenomena for the volume, intrinsic volumes, or more general measures of the convex hulls of these random point sets, as the space dimension [Formula: see text] tends to infinity. The dual setting of polytopes generated by random halfspaces is also investigated.

Discussions

• How do random shapes behave as dimensions grow? “Threshold phenomena for high-dimensional random polytopes” studies convex hulls of random points and identifies sharp changes in geometric measures su [bsky, 1 points, 0 comments]

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