Angles of random simplices and face numbers of random polytopes
Sign Up to like & getrecommendations! Published in 2019 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2021.107612
Abstract: Pick $d+1$ points uniformly at random on the unit sphere in $\mathbb R^d$. What is the expected value of the angle sum of the simplex spanned by these points? Choose $n$ points uniformly at random… read more here.
Keywords: face numbers; beta; random polytopes; angles random ... See more keywords
Limit theorems for random polytopes with vertices on convex surfaces
Sign Up to like & getrecommendations! Published in 2018 at "Advances in Applied Probability"
DOI: 10.1017/apr.2018.58
Abstract: Abstract We consider the random polytope Kn, defined as the convex hull of n points chosen independently and uniformly at random on the boundary of a smooth convex body in ℝd. We present both lower… read more here.
Keywords: polytopes vertices; theorems random; limit theorems; vertices convex ... See more keywords