A0592
Title: The volume of random Beta polytopes in high dimensions
Authors: Nicola Turchi - University of Milano-Bicocca (Italy) [presenting]
Gilles Bonnet - University of Groningen (Netherlands)
Zakhar Kabluchko - University of Muenster (Germany)
Abstract: Beta polytopes are a class of random polytopes which arise as convex hulls of independent random points distributed according to a certain radially-symmetric probability distribution supported on the Euclidean ball, called the beta distribution. As the space dimension grows, the expected fraction of the volume that these polytopes fill within their supporting balls can be asymptotically negligible or not, depending on the number of points picked in each dimension. An overview of how to quantify this statement is given, first showing a rough threshold for the aforementioned growth and, secondly, a more precise one, namely, how many points are needed to get any fraction in average.
