50 years sets with positive reach -- a survey.
A counterexample for the optimality of Kendall-Cranston coupling.
A Gaussian Correlation Inequality for Certain Bodies in Rn .
A geometric approach for convexity in some variational problem in the Gauss space
A limit theorem for the position of a particle in the Lorentz model.
A note on the existence of Gibbs marked point processes with applications in stochastic geometry
This paper generalizes a recent existence result for infinite-volume marked Gibbs point processes. We try to use the existence theorem for two models from stochastic geometry. First, we show the existence of Gibbs facet processes in with repulsive interactions. We also prove that the finite-volume Gibbs facet processes with attractive interactions need not exist. Afterwards, we study Gibbs-Laguerre tessellations of . The mentioned existence result cannot be used, since one of its assumptions...
A Remark on Buffon's Needle Problem.
A Simple Proof of the Kinematic Formula.
A Simpler Proof of the Negative Association Property for Absolute Values of Measures Tied to Generalized Orlicz Balls
Negative association for a family of random variables means that for any coordinatewise increasing functions f,g we have for any disjoint sets of indices (iₘ), (jₙ). It is a way to indicate the negative correlation in a family of random variables. It was first introduced in 1980s in statistics by Alem Saxena and Joag-Dev Proschan, and brought to convex geometry in 2005 by Wojtaszczyk Pilipczuk to prove the Central Limit Theorem for Orlicz balls. The paper gives a relatively simple proof of...
A simplified proof of a conjecture of D. G. Kendall concerning shapes of random polygons.
Almost sure asymptotic behaviour of the -neighbourhood surface area of Brownian paths
We show that whenever the -dimensional Minkowski content of a subset exists and is finite and positive, then the “S-content” defined analogously as the Minkowski content, but with volume replaced by surface area, exists as well and equals the Minkowski content. As a corollary, we obtain the almost sure asymptotic behaviour of the surface area of the Wiener sausage in , .
An affine embedding of the gamma manifold.
An approximation of the κ-function for the study of binary images.
Jensen et al. (1990) gave an exact expression for the κ-function in non-overlapping Boolean models. The present study proposes and evaluates an approximate expression for the κ-function in overlapping isotropic Boolean models based on an approximation of the covariogram of the primary grain. We study the suitability of a Boolean model for two binary images using this approximate expression.
An Elementary Approach to Lower Bounds in Geometric Discrepancy.
An explicit formula about the convex hull of random points.
An incomplete Voronoi tessellation
This paper presents distributional properties of a random cell structure which results from a growth process. It starts at the points of a Poisson point process. The growth is spherical with identical speed for all points; it stops whenever the boundaries of different cells have contact. The whole process finally stops after time t. So the space is not completely filled with cells, and the cells have both planar and spherical boundaries. Expressions are given for contact distribution functions,...
Appendice : « Décomposition en produit de deux browniens d'une martingale à valeurs dans un groupe muni d'une métrique bi-invariante »
Approximation of Zonoids by Zonotopes in Fixed Directions.
Approximation on convex bodies by random polytopes.
Aproximación aleatoria de cuerpos convexos.
Problems related to the random approximation of convex bodies fall into the field of integral geometry and geometric probabilities. The aim of this paper is to give a survey of known results about the stochastic model that has received special attention in the literature and that can be described as follows:Let K be a d-dimensional convex body in Eucliden space Rd, d ≥ 2. Denote by Hn the convex hull of n independent random points X1, ..., Xn distributed identically and uniformly in the interior...