Search Results for author: Christoph Thäle

Found 2 papers, 0 papers with code

Sharp inequalities for the mean distance of random points in convex bodies

no code implementations7 Oct 2020 Gilles Bonnet, Anna Gusakova, Christoph Thäle, Dmitry Zaporozhets

For a convex body $K\subset\mathbb{R}^d$ the mean distance $\Delta(K)=\mathbb{E}|X_1-X_2|$ is the expected Euclidean distance of two independent and uniformly distributed random points $X_1, X_2\in K$.

Metric Geometry Probability Primary: 52A22, 52A40, 53C65, Secondary: 60D05

Weak convergence of the intersection point process of Poisson hyperplanes

no code implementations13 Jul 2020 Anastas Baci, Gilles Bonnet, Christoph Thäle

Implications on the weak convergence of the convex hull of the intersection point process and the convergence of its $f$-vector are also discussed, disproving and correcting thereby a conjecture of Devroye and Toussaint [J.\ Algorithms 14. 3 (1993), 381--394] in computational geometry.

Probability Primary 60D05, 60F05, Secondary 52A22, 53C65

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