For convex bodies $K$ with $\mathcal{C}^2$ boundary in $\mathbb{R}^d$, we provide results on the volume of random polytopes with vertices chosen along the boundary of $K$ which we call $\textit{random inscribing polytopes}$. In particular, we prove results concerning the variance and higher moments of the volume, as well as show that the random inscribing polytopes generated by the Poisson process satisfy central limit theorem
International audienceRandom polytopes have constituted some of the central objects of stochastic ge...
International audienceWe consider the convex hull of the perturbed point process comprised of $n$ i....
We consider motion-invariant (i.e. stationary and isotropic) Poisson hyperplane processes subdividin...
International audienceFor convex bodies $K$ with $\mathcal{C}^2$ boundary in $\mathbb{R}^d$, we prov...
AbstractFor convex bodies K with C2 boundary in Rd, we explore random polytopes with vertices chosen...
For convex bodies K with C2 boundary and everywhere positive Gauß-Kronecker curvature in Rd, we expl...
We prove the central limit theorem for the volume and the f-vector of the random polytope Pn and the...
We consider the random polytope \(\it K_{n}\), defined as the convex hull of \(\it n\) points chosen...
We establish central limit theorems for natural volumes of random inscribed polytopes in projective ...
AbstractLet K be a smooth convex set with volume one in Rd. Choose n random points in K independentl...
Choose n independent random points on the boundary of a convex body K ⊂ Rd. The intersection of the ...
AbstractA random polytope is the convex hull of uniformly distributed random points in a convex body...
The convex hull of $N$ independent random points chosen on the boundary of a simple polytope in $ \m...
We construct and investigate random geometric structures that are based on a homogeneous Poisson poi...
Let $K \subset \R^d$ be a smooth convex set and let $\P_\la$ be a Poisson point process on $\R^d$ of...
International audienceRandom polytopes have constituted some of the central objects of stochastic ge...
International audienceWe consider the convex hull of the perturbed point process comprised of $n$ i....
We consider motion-invariant (i.e. stationary and isotropic) Poisson hyperplane processes subdividin...
International audienceFor convex bodies $K$ with $\mathcal{C}^2$ boundary in $\mathbb{R}^d$, we prov...
AbstractFor convex bodies K with C2 boundary in Rd, we explore random polytopes with vertices chosen...
For convex bodies K with C2 boundary and everywhere positive Gauß-Kronecker curvature in Rd, we expl...
We prove the central limit theorem for the volume and the f-vector of the random polytope Pn and the...
We consider the random polytope \(\it K_{n}\), defined as the convex hull of \(\it n\) points chosen...
We establish central limit theorems for natural volumes of random inscribed polytopes in projective ...
AbstractLet K be a smooth convex set with volume one in Rd. Choose n random points in K independentl...
Choose n independent random points on the boundary of a convex body K ⊂ Rd. The intersection of the ...
AbstractA random polytope is the convex hull of uniformly distributed random points in a convex body...
The convex hull of $N$ independent random points chosen on the boundary of a simple polytope in $ \m...
We construct and investigate random geometric structures that are based on a homogeneous Poisson poi...
Let $K \subset \R^d$ be a smooth convex set and let $\P_\la$ be a Poisson point process on $\R^d$ of...
International audienceRandom polytopes have constituted some of the central objects of stochastic ge...
International audienceWe consider the convex hull of the perturbed point process comprised of $n$ i....
We consider motion-invariant (i.e. stationary and isotropic) Poisson hyperplane processes subdividin...
DOI
Add to ORKG