Let X1,.,XN, N > n, be independent random points in ℝn, 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 n tends to infinity. The dual setting of polytopes generated by random halfspaces is also investigated.

Bonnet, G., Chasapis, G., Grote, J., Temesvari, D., Turchi, N. (2019). Threshold phenomena for high-dimensional random polytopes. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 21(5) [10.1142/S0219199718500384].

Threshold phenomena for high-dimensional random polytopes

Turchi N.
2019

Abstract

Let X1,.,XN, N > n, be independent random points in ℝn, 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 n tends to infinity. The dual setting of polytopes generated by random halfspaces is also investigated.
Articolo in rivista - Articolo scientifico
Beta distribution; beta-prime distribution; convex bodies; isotropic log-concave measures; phase transition; random polytopes; volume threshold;
English
2019
21
5
1850038
none
Bonnet, G., Chasapis, G., Grote, J., Temesvari, D., Turchi, N. (2019). Threshold phenomena for high-dimensional random polytopes. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 21(5) [10.1142/S0219199718500384].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/395179
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