Threshold phenomena for high-dimensional random polytopes-Reference-Cited by-同舟云学术

Threshold phenomena for high-dimensional random polytopes

Published:2019-07-12 Issue:05 Volume:21 Page:1850038
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

Bonnet Gilles¹,Chasapis Giorgos²,Grote Julian¹,Temesvari Daniel¹,Turchi Nicola¹

Affiliation:

1. Faculty of Mathematics, Ruhr University Bochum, Universitätsstraße 150, 44780 Bochum, Germany

2. Department of Mathematics, National & Kapodistrian University of Athens, Panepistimioupolis, Zografou 15784, Athens, Greece

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199718500384

Reference14 articles.

1. The central limit problem for convex bodies

2. On 0-1 Polytopes with Many Facets

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4. Geometry of Isotropic Convex Bodies

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