| HAL-Inria | Publications, software ... of Inria's scientists |
Journal articles
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.
https://hal.inria.fr/hal-02937527
Contributor : Xavier Goaoc Connect in order to contact the contributor
Submitted on : Monday, September 14, 2020 - 10:11:25 AM
Last modification on : Friday, February 4, 2022 - 9:00:13 AM
Contributor : Xavier Goaoc Connect in order to contact the contributor
Submitted on : Monday, September 14, 2020 - 10:11:25 AM
Last modification on : Friday, February 4, 2022 - 9:00:13 AM
Links full text
