Threshold phenomena for high-dimensional random polytopes

Gilles Bonnet*, Giorgos Chasapis, Julian Grote, Daniel Temesvari, Nicola Turchi

*Corresponding author voor dit werk

Onderzoeksoutput: Article โ€บ Academic โ€บ peer review

14 Citaten (Scopus)

Samenvatting

Let ๐‘‹1,โ€ฆ,๐‘‹๐‘, ๐‘>๐‘›, be independent random points in โ„๐‘›, 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 ๐‘› tends to infinity. The dual setting of polytopes generated by random halfspaces is also investigated.
Originele taal-2English
Artikelnummer1850038
TijdschriftCommunications in Contemporary Mathematics
Volume21
Nummer van het tijdschrift5
DOI's
StatusPublished - 2019
Extern gepubliceerdJa

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