Add to ORKGAssume K ⊂ Rd is a convex body and X is a (large) finite subset of K. How many convex polytopes are there whose vertices belong to X? Is there a typical shape of such polytopes? How well does the maximal such polytope (which is actually the convex hull of X) approximate K? We are interested in these questions mainly in two cases. The first is when X is a random sample of n uniform, independent points from K. In this case motivation comes from Sylvester’s famous four-point problem and from the theory of random polytopes. The second case is when X = K ∩ Zd where Zd is the lattice of integer points in Rd and the questions come from integer programming and geometry of numbers. Surprisingly (or not so surprisingly), the answers in the two cases ...
International audienceWe examine how the measure and the number of vertices of the convex hull of a ...
Random polytopes can be constructed in many different ways. In this thesis two certain kinds are con...
We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ p...
Summary. Denote by E, the convex hull of n points chosen uniformly and independently from the d-dime...
Abstract. A random polytope, Kn, is the convex hull of n points chosen randomly, independently, and ...
We consider the random polytope \(\it K_{n}\), defined as the convex hull of \(\it n\) points chosen...
AbstractChoose n random points in Rd, let Pn be their convex hull, and denote by fi(Pn) the number o...
The convex hull of $N$ independent random points chosen on the boundary of a simple polytope in $ \m...
The convex hull of $N$ independent random points chosen on the boundary of a simple polytope in $ \m...
Let K ⊂ Rd be a sufficiently round convex body (the ratio of the circumscribed ball to the inscribed...
International audienceWe examine how the measure and the number of vertices of the convex hull of a ...
International audienceWe examine how the measure and the number of vertices of the convex hull of a ...
International audienceWe examine how the measure and the number of vertices of the convex hull of a ...
International audienceWe examine how the measure and the number of vertices of the convex hull of a ...
International audienceWe examine how the measure and the number of vertices of the convex hull of a ...
International audienceWe examine how the measure and the number of vertices of the convex hull of a ...
Random polytopes can be constructed in many different ways. In this thesis two certain kinds are con...
We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ p...
Summary. Denote by E, the convex hull of n points chosen uniformly and independently from the d-dime...
Abstract. A random polytope, Kn, is the convex hull of n points chosen randomly, independently, and ...
We consider the random polytope \(\it K_{n}\), defined as the convex hull of \(\it n\) points chosen...
AbstractChoose n random points in Rd, let Pn be their convex hull, and denote by fi(Pn) the number o...
The convex hull of $N$ independent random points chosen on the boundary of a simple polytope in $ \m...
The convex hull of $N$ independent random points chosen on the boundary of a simple polytope in $ \m...
Let K ⊂ Rd be a sufficiently round convex body (the ratio of the circumscribed ball to the inscribed...
International audienceWe examine how the measure and the number of vertices of the convex hull of a ...
International audienceWe examine how the measure and the number of vertices of the convex hull of a ...
International audienceWe examine how the measure and the number of vertices of the convex hull of a ...
International audienceWe examine how the measure and the number of vertices of the convex hull of a ...
International audienceWe examine how the measure and the number of vertices of the convex hull of a ...
International audienceWe examine how the measure and the number of vertices of the convex hull of a ...
Random polytopes can be constructed in many different ways. In this thesis two certain kinds are con...
We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ p...