78 citations · 138 across the 27 of their papers we have counts for
28 papers · 1 filter
Expected mixed volumes of convex hulls of random walks and Lévy processes
Artyom Bolotin, Dmitry Zaporozhets
Let be the convex hulls of independent partial-sum processes in whose increments are exchangeable within each process. We express the expected mixed…
Angle sums of random polytopes
Thomas Godland, Zakhar Kabluchko, Dmitry Zaporozhets
For two families of random polytopes we compute explicitly the expected sums of the conic intrinsic volumes and the Grassmann angles at all faces of any given dimension of the poly…
Random sections of spherical convex bodies
Tatiana Moseeva, Alexander Tarasov, Dmitry Zaporozhets
Let be a convex spherical body. Denote by the distance between two random points in and denote by the length of a random chord of . W…
Convex hulls of several multidimensional Gaussian random walks
Julien Randon-Furling, Dmitry Zaporozhets
We derive explicit formulae for the expected volume and the expected number of facets of the convex hull of several multidimensional Gaussian random walks in terms of the Gaussian…
An improved multivariate version of Kolmogorov's second uniform limit theorem
Friedrich Götze, Andrei Yu. Zaitsev, Dmitry Zaporozhets
The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent summands by infinitely divisible laws may be t…
Grassmann angles and absorption probabilities of Gaussian convex hulls
Friedrich Götze, Zakhar Kabluchko, Dmitry Zaporozhets
Let be an arbitrary subset in with a conic (or positive) hull . Consider its Gaussian image , where is a -matrix whose entries are independe…