Creative Commons Attribution-ShareAlike 4.0 International
This Work, Asymptotic properties of random polytopes, by Admin Admin is licensed under a Creative Commons Attribution-ShareAlike 4.0 International license.

Asymptotic properties of random polytopes


Asymptotic properties of random polytopes
Publication details: 
Random polytopes have constituted some of the central objects of stochastic geometry for more than 150 years. They are in general generated as convex hulls of a random set of points in the Euclidean space. The study of such models requires the use of ingredients coming from both convex geometry and probability theory. In the last decades, the study has been focused on their asymptotic properties and in particular expectation and variance estimates. In several joint works with Tomasz Schreiber and J. E. Yukich, we have investigated the scaling limit of several models (uniform model in the unit-ball, uniform model in a smooth convex body, Gaussian model) and have deduced from it limiting variances for several geometric characteristics including the number of k-dimensional faces and the volume. In this paper, we survey the most recent advances on these questions and we emphasize the particular cases of random polytopes in the unit-ball and Gaussian polytopes.
Source et DOI
Vidéo
Voir la vidéo
Asymptotic properties of random polytopes
Groups: