In this paper we introduce a new sequence of quantities for random polytopes. Let $K_N=\conv\{X_1,...,X_N\}$ be a random polytope generated by independent random vectors uniformly distributed in an isotropic convex body K of $\R^n$. We prove that the so-called k-th mean outer radius R˜k(KN) has order max{k−−√,logN−−−−−√}LK with high probability if n2≤N≤en√. We also show that this is also the right order of the expected value of R˜k(KN) in the full range n≤N≤en√
For convex bodies K with C2 boundary and everywhere positive Gauß-Kronecker curvature in Rd, we expl...
AbstractChoose n random points in Rd, let Pn be their convex hull, and denote by fi(Pn) the number o...
We study the expected value of support functions of random polytopes in a certain direction, where ...
In this paper we introduce a new sequence of quantities for random polytopes. Let $K_N=\conv\{X_1,.....
In this paper we introduce a new sequence of quantities for random polytopes. Let KN = conv{X1, . ....
AbstractLet K be a convex body in Rd and let Xn=(x1,…,xn) be a random sample of n independent points...
AbstractLet K be an isotropic convex body in Rn and let Zq(K) be the Lq-centroid body of K. For ever...
Let X1,…,XN be independent random vectors uniformly distributed on an isotropic convex body K ⊂ Rn, ...
We show that the expected value of the mean width of a random polytope generated by $ N$ random vect...
Abstract. For a given convex body K in Rd, a random polytope K(n) is defined (essentially) as the in...
Let X1,..., XN be independent random vectors uniformly dis-tributed on an isotropic convex body K ⊂ ...
We prove some “high probability” results on the expected value of the mean width for random perturba...
In this work we study a class of random convex sets that "interpolate" between polytopes and zonotop...
Let μ be a log-concave probability measure on Rn and for any N> n consider the random polytop...
We consider the random polytope \(\it K_{n}\), defined as the convex hull of \(\it n\) points chosen...
For convex bodies K with C2 boundary and everywhere positive Gauß-Kronecker curvature in Rd, we expl...
AbstractChoose n random points in Rd, let Pn be their convex hull, and denote by fi(Pn) the number o...
We study the expected value of support functions of random polytopes in a certain direction, where ...
In this paper we introduce a new sequence of quantities for random polytopes. Let $K_N=\conv\{X_1,.....
In this paper we introduce a new sequence of quantities for random polytopes. Let KN = conv{X1, . ....
AbstractLet K be a convex body in Rd and let Xn=(x1,…,xn) be a random sample of n independent points...
AbstractLet K be an isotropic convex body in Rn and let Zq(K) be the Lq-centroid body of K. For ever...
Let X1,…,XN be independent random vectors uniformly distributed on an isotropic convex body K ⊂ Rn, ...
We show that the expected value of the mean width of a random polytope generated by $ N$ random vect...
Abstract. For a given convex body K in Rd, a random polytope K(n) is defined (essentially) as the in...
Let X1,..., XN be independent random vectors uniformly dis-tributed on an isotropic convex body K ⊂ ...
We prove some “high probability” results on the expected value of the mean width for random perturba...
In this work we study a class of random convex sets that "interpolate" between polytopes and zonotop...
Let μ be a log-concave probability measure on Rn and for any N> n consider the random polytop...
We consider the random polytope \(\it K_{n}\), defined as the convex hull of \(\it n\) points chosen...
For convex bodies K with C2 boundary and everywhere positive Gauß-Kronecker curvature in Rd, we expl...
AbstractChoose n random points in Rd, let Pn be their convex hull, and denote by fi(Pn) the number o...
We study the expected value of support functions of random polytopes in a certain direction, where ...
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