Limit theorems for generalized convex hulls
DOI:
https://doi.org/10.17721/1812-5409.2025/2.9Keywords:
generalized convexity, Poisson hyperplane tesselation, zero cell, curvature measureAbstract
The (K, H)-hull of a set A ⊆ Rd is a generalization of the standard closed convex hull of A which can be defined as the intersection of all images that contain A of a closed convex subset K ⊂ Rd under the action of a subset H of the group of invertible affine transformations of Rd. We demonstrate that the scaled normalization of the (K, H)-hull of a random sample, distributed according to a probability measure µ on K with a power-like behavior near the boundary ∂K of K, converges in distribution to a random closed set which can be viewed as the zero cell of a certain Poisson hyperplane tessellation with explicit intensity measure.
Pages of the article in the issue: 73 - 81
Language of the article: English
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