A random spherical polytope Pn in a spherically convex set K⊂Sd as considered here is the spherical convex hull of n independent, uniformly distributed random points in K. The behaviour of Pn for a spherically convex set K contained in an open halfsphere is quite similar to that of a similarly generated random convex polytope in a Euclidean space, but the case when K is a halfsphere is different. This is what we investigate here, establishing the asymptotic behaviour, as n tends to infinity, of the expectation of several characteristics of Pn, such as facet and vertex number, volume and surface area. For the Hausdorff distance from the halfsphere, we obtain also some almost sure asymptotic estimates. © 2016 Wiley Periodicals, Inc
In this work we study a class of random convex sets that "interpolate" between polytopes and zonotop...
In this work we study a class of random convex sets that "interpolate" between polytopes and zonotop...
In this paper we prove asymptotic upper bounds on the variance of the number of vertices and missed ...
A random spherical polytope Pn in a spherically convex set inline image as considered here is the sp...
AbstractThe convex hull of a set of independent random points sampled from three types of sphericall...
Facets of the convex hull of n independent random vectors chosen uniformly at random from the unit s...
Facets of the convex hull of n independent random vectors chosen uniformly at random from the unit s...
Facets of the convex hull of n independent random vectors chosen uniformly at random from the unit s...
Facets of the convex hull of n independent random vectors chosen uniformly at random from the unit s...
AbstractFor convex bodies K with C2 boundary in Rd, we explore random polytopes with vertices chosen...
Asymptotic formulas are proved for the expected $T$-functional of the convex hull of independent and...
Asymptotic formulas are proved for the expected $T$-functional of the convex hull of independent and...
AbstractThe mean volume and the mean surface area of the convex hull of n random points chosen indep...
Choose n independent random points on the boundary of a convex body K ⊂ Rd. The intersection of the ...
In this work we study a class of random convex sets that "interpolate" between polytopes and zonotop...
In this work we study a class of random convex sets that "interpolate" between polytopes and zonotop...
In this work we study a class of random convex sets that "interpolate" between polytopes and zonotop...
In this paper we prove asymptotic upper bounds on the variance of the number of vertices and missed ...
A random spherical polytope Pn in a spherically convex set inline image as considered here is the sp...
AbstractThe convex hull of a set of independent random points sampled from three types of sphericall...
Facets of the convex hull of n independent random vectors chosen uniformly at random from the unit s...
Facets of the convex hull of n independent random vectors chosen uniformly at random from the unit s...
Facets of the convex hull of n independent random vectors chosen uniformly at random from the unit s...
Facets of the convex hull of n independent random vectors chosen uniformly at random from the unit s...
AbstractFor convex bodies K with C2 boundary in Rd, we explore random polytopes with vertices chosen...
Asymptotic formulas are proved for the expected $T$-functional of the convex hull of independent and...
Asymptotic formulas are proved for the expected $T$-functional of the convex hull of independent and...
AbstractThe mean volume and the mean surface area of the convex hull of n random points chosen indep...
Choose n independent random points on the boundary of a convex body K ⊂ Rd. The intersection of the ...
In this work we study a class of random convex sets that "interpolate" between polytopes and zonotop...
In this work we study a class of random convex sets that "interpolate" between polytopes and zonotop...
In this work we study a class of random convex sets that "interpolate" between polytopes and zonotop...
In this paper we prove asymptotic upper bounds on the variance of the number of vertices and missed ...