In the 1980s, Diaconis and Freedman studied the low-dimensional projections of random
vectors from the Euclidean unit sphere and the simplex in high dimensions, noting that the …

The random convex hull of a Poisson point process in R d whose intensity measure is a
multiple of the standard Gaussian measure on R d is investigated. The purpose of this paper …

A new characterization of the exponential type Orlicz spaces generated by the functions\exp
(| x|^ p)-1 exp (| x| p)-1 (p ≥ 1 p≥ 1) is given. We define norms for centered random …

For an isotropic convex body K⊂ R n we consider the isotropic constant LKN of the
symmetric random polytope KN generated by N independent random points which are …

Facets of the convex hull of n independent random vectors chosen uniformly at random from
the unit sphere in R d R^d are studied. A particular focus is given on the height of the facets …

A question related to some conjectures of Lutwak about the affine quermassintegrals of a
convex body K in R n asks whether for every convex body K in R n and all 1⩽ k⩽ n Φ [k](K) …

In this paper we further develop the theory of f-divergences for log-concave functions and
their related inequalities. We establish Pinsker inequalities and new affine invariant entropy …

In this work we study a class of random convex sets that “interpolate” between polytopes and
zonotopes. These sets arise from considering aqt h-moment (q≥ 1) of an average of order …

In this chapter we introduce the topic of random polytopes and some of the problems that
this subject handles. From a methodical point of view, the study of random polytopes …

This chapter begins with a general introduction into the theory of stochastic geometry and
random polytopes, presenting some milestones in their historical development. In particular …