Phase transition for the volume of high-dimensional random polytopes

Gilles Bonnet, Zakhar Kabluchko, Nicola Turchi*

*Corresponding author voor dit werk

OnderzoeksoutputAcademicpeer review

8 Citaten (Scopus)

Samenvatting

The beta polytope (Formula presented.) is the convex hull of n i.i.d. random points distributed in the unit ball of (Formula presented.) according to a density proportional to (Formula presented.) if (Formula presented.) (in particular, (Formula presented.) corresponds to the uniform distribution in the ball), or uniformly on the unit sphere if (Formula presented.). We show that the expected normalized volumes of high-dimensional beta polytopes exhibit a phase transition and we describe its shape. We derive analogous results for the intrinsic volumes of beta polytopes and, when (Formula presented.), their number of vertices.

Originele taal-2English
Pagina's (van-tot)648-663
Aantal pagina's16
TijdschriftRandom structures & algorithms
Volume58
Nummer van het tijdschrift4
Vroegere onlinedatum28-dec.-2020
DOI's
StatusPublished - jul.-2021
Extern gepubliceerdJa

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