Conic support measures

Schneider, Rolf

doi:10.1016/j.jmaa.2018.11.017

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2020

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Cited by 2 publications

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References 24 publications

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“…d , where the sphere is endowed with the geodesic distance (alternatively, the angular Hausdorff distance as introduced in[31] can be used as well). The space K con can be identified with the space K s of spherically convex sets (to use the notation of [32, Section 6.5]) by identifying each closed convex cone C = {0} with the spherically convex set C ∩ S d .Proof of Lemma 3.1.…”

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confidence: 99%

A new approach to weak convergence of random cones and polytopes

Kabluchko,

Temesvari,

Thäle

2020

Preprint

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A new approach to prove weak convergence of random polytopes on the space of compact convex sets is presented. This is used to show that the profile of the rescaled Schläfli random cone of a random conical tessellation generated by n independent and uniformly distributed random linear hyperplanes in R d+1 weakly converges to the typical cell of a stationary and isotropic Poisson hyperplane tessellation in R d , as n → ∞.

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confidence: 99%