Random polytopes and the wet part for arbitrary probability distributions - Archive ouverte HAL Access content directly
Reports (Research Report) Year : 2019

## Random polytopes and the wet part for arbitrary probability distributions

(1) , (2) , (3) , (4) , (5)
1
2
3
4
5
Imre Barany
• Function : Author
• PersonId : 864878
• Function : Author
• PersonId : 929931
Xavier Goaoc
Alfredo Hubard
• Function : Author
Günter Rote

#### Abstract

We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ points from an arbitrary probability measure in $\mathbf{R}^d$ relates to the wet part of that measure. This extends classical results for the uniform distribution from a convex set [B\'ar\'any and Larman 1988]. The lower bound of B\'ar\'any and Larman continues to hold in the general setting, but the upper bound must be relaxed by a factor of $\log n$. We show by an example that this is tight.

### Dates and versions

hal-02050632 , version 1 (27-02-2019)

### Identifiers

• HAL Id : hal-02050632 , version 1
• ARXIV :

### Cite

Imre Barany, Matthieu Fradelizi, Xavier Goaoc, Alfredo Hubard, Günter Rote. Random polytopes and the wet part for arbitrary probability distributions. [Research Report] Rényi Institute of Mathematics; University College London; Université Paris-Est; Université de Lorraine; Freie Universität Berlin. 2019. ⟨hal-02050632⟩

### Export

BibTeX TEI Dublin Core DC Terms EndNote Datacite

156 View