Geodesic
A new approach to weak convergence of random cones and polytopes
Canadian journal of mathematics, Tome 73 (2021) no. 6, pp. 1627-1647

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DOI

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 $\mathbb {R}^{d+1}$, weakly converges to the typical cell of a stationary and isotropic Poisson hyperplane tessellation in $\mathbb {R}^d$, as $n\to \infty $.
DOI : 10.4153/S0008414X20000620
Mots-clés : Cover–Efron cone, random cone, random polytope, random tessellation, Scheffé’s lemma, Schläfli cone, stochastic geometry, typical cell, weak convergence 
Kabluchko, Zakhar; Temesvari, Daniel; Thäle, Christoph. A new approach to weak convergence of random cones and polytopes. Canadian journal of mathematics, Tome 73 (2021) no. 6, pp. 1627-1647. doi: 10.4153/S0008414X20000620
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     title = {A new approach to weak convergence of random cones and polytopes},
     journal = {Canadian journal of mathematics},
     pages = {1627--1647},
     year = {2021},
     volume = {73},
     number = {6},
     doi = {10.4153/S0008414X20000620},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X20000620/}
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