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Results tagged with convex-geometry
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user 30800
A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...
5
votes
Continuity of barycentre in Hausdorff metric
This question has been first discussed in the paper [ABB] below. They show that, in the plane, the barycenter of the boundary has the desired property: It is Lipschitz-continuous with respect to the …
- 1,083
1
vote
An elementary probability question
YES, trivially. Even $E(\|X_0-X_1\|^2)$ is already bounded by 4x the variance. (or even 2x ?)
For $n < d$, this is optimal up to a constant factor. Take the uniform distribution on the $d$ unit vecto …
- 1,083
1
vote
Accepted
Expected minimum face angle of random convex polyhedron in $\mathbb{R}^3$
The answer is YES. (I am assuming you mean the angle between two adjacent edges on a common face. (The dihedral angles all go to $\pi$.)) The easy and brief reason is that, in a large random point set …
- 1,083