Threshold phenomena for high-dimensional random polytopes
| Autor: | Julian Grote, Nicola Turchi, Daniel Temesvari, Gilles Bonnet, Giorgos Chasapis |
|---|---|
| Přispěvatelé: | Bonnet, G, Chasapis, G, Grote, J, Temesvari, D, Turchi, N |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Phase transition
beta-prime distribution Applied Mathematics General Mathematics Probability (math.PR) Metric Geometry (math.MG) Polytope Beta prime distribution High dimensional Beta distribution random polytope Combinatorics Distribution (mathematics) Mathematics - Metric Geometry phase transition 52A23 52B11 52A22 60D05 FOS: Mathematics Random points volume threshold Beta (velocity) convex bodie isotropic log-concave measure Mathematics - Probability Mathematics |
| Popis: | Let $X_1,\ldots,X_N$, $N>n$, be independent random points in $\mathbb{R}^n$, 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. 26 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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