Random polytopes and the wet part for arbitrary probability distributions

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

https://hal.inria.fr/hal-02050632
Contributor : Xavier Goaoc <>
Submitted on : Wednesday, February 27, 2019 - 11:52:18 AM
Last modification on : Friday, June 7, 2019 - 4:32:47 PM

Links full text

Identifiers

  • HAL Id : hal-02050632, version 1
  • ARXIV : 1902.06519

Citation

Imre Barany, Matthieu Fradelizi, Xavier Goaoc, Alfredo Hubard, Günter Rote. Random polytopes and the wet part for arbitrary probability distributions. 2019. ⟨hal-02050632⟩

Share

Metrics

Record views

80