AbstractA random polytope is the convex hull of uniformly distributed random points in a convex body K. A general lower bound on the variance of the volume and f-vector of random polytopes is proved. Also an upper bound in the case when K is a polytope is given. For polytopes, as for smooth convex bodies, the upper and lower bounds are of the same order of magnitude. The results imply a law of large numbers for the volume and f-vector of random polytopes when K is a polytope
International audienceWe examine how the measure and the number of vertices of the convex hull of a ...
We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ p...
We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ p...
AbstractA random polytope is the convex hull of uniformly distributed random points in a convex body...
We consider the random polytope \(\it K_{n}\), defined as the convex hull of \(\it n\) points chosen...
We prove the central limit theorem for the volume and the f-vector of the random polytope Pn and the...
International audienceRandom polytopes have constituted some of the central objects of stochastic ge...
International audienceRandom polytopes have constituted some of the central objects of stochastic ge...
AbstractLet K be a convex body in Rd and let Xn=(x1,…,xn) be a random sample of n independent points...
Let $K \subset \R^d$ be a smooth convex set and let $\P_\la$ be a Poisson point process on $\R^d$ of...
Let $K \subset \R^d$ be a smooth convex set and let $\P_\la$ be a Poisson point process on $\R^d$ of...
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 ...
For convex bodies K with C2 boundary and everywhere positive Gauß-Kronecker curvature in Rd, we expl...
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 ...
We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ p...
We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ p...
AbstractA random polytope is the convex hull of uniformly distributed random points in a convex body...
We consider the random polytope \(\it K_{n}\), defined as the convex hull of \(\it n\) points chosen...
We prove the central limit theorem for the volume and the f-vector of the random polytope Pn and the...
International audienceRandom polytopes have constituted some of the central objects of stochastic ge...
International audienceRandom polytopes have constituted some of the central objects of stochastic ge...
AbstractLet K be a convex body in Rd and let Xn=(x1,…,xn) be a random sample of n independent points...
Let $K \subset \R^d$ be a smooth convex set and let $\P_\la$ be a Poisson point process on $\R^d$ of...
Let $K \subset \R^d$ be a smooth convex set and let $\P_\la$ be a Poisson point process on $\R^d$ of...
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 ...
For convex bodies K with C2 boundary and everywhere positive Gauß-Kronecker curvature in Rd, we expl...
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 ...
We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ p...
We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ p...
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