Variance asymptotics for random polytopes in smooth convex bodies
type: Dataset
description: Let $K \subset \R^d$ be a smooth convex set and let $\P_\la$ be a Poisson point process on $\R^d$ of intensity $\la$. The convex hull of $\P_\la \cap K$ is a random convex polytope $K_\la$. As $\la \to \infty$, we show that the variance of the number of $k$-dimensional faces of $K_\la$, when properly scaled, converges to a scalar multiple of the affine surface area of $K$. Similar asymptotics hold for the variance of the number of $k$-dimensional faces for the convex hull of a binomial process in $K$.
issued: 2026-05-15T15:04:33.326121
language: en
modified: 2026-05-15T15:04:33.326126
contact point: Organization
  fn: CCSD
keyword: infoeu-reposemanticspreprint
keyword: mathmath-prmathematics-mathprobability-mathpr
keyword: preprints-working-papers-
landing page: https://hal.science/hal-00710266

Variance asymptotics for random polytopes in smooth convex bodies
type: Distribution
format: HTML
issued: 2026-05-15T15:04:33.329455
modified: 2026-05-15T15:04:33.318302
access URL: https://hal.science/hal-00710266

test_moissonnage_selune
type: Agent