Random walks that avoid their past convex hull.
Rareté des intervalles recouvrant un point dans un recouvrement aléatoire
Regular Simplices and Gaussian Samples.
Section and Projection Means of Convex Bodies.
Self-similar and Markov composition structures.
Simplices rarely contain their circumcenter in high dimensions
Acute triangles are defined by having all angles less than , and are characterized as the triangles containing their circumcenter in the interior. For simplices of dimension , acuteness is defined by demanding that all dihedral angles between -dimensional faces are smaller than . However, there are, in a practical sense, too few acute simplices in general. This is unfortunate, since the acuteness property provides good qualitative features for finite element methods. The property of acuteness...
Some geometric probability problems involving the Eulerian numbers.
Stability Properties of Cauchy's Surface Area Formula.
Stereology of dihedral angles
The paper presents a short survey of stereological problems concerning dihedral angles, their solutions and applications, and introduces a graph for determining the distribution functions of planar angles under the hypothesis that dihedral angles in are of the same size and create a random field.
Stereology of grain boundary precipitates
Precipitates modelled by rotary symmetrical lens-shaped discs are situated on matrix grain boundaries and the homogeneous specimen is intersected by a plate section. The stereological model presented enables one to express all basic parameters of spatial structure and moments of the corresponding probability distributions of quantitative characteristics of precipitates in terms of planar structure parameters the values of which can be estimated from measurements carried out in the plane section....
Stochastical Approximation of Convex Bodies.
Systems of stochastically independent and normally distributed random points in the Euclidean space .
The determination of convex bodies from the size and shape of their projections and sections
We survey results concerning the extent to which information about a convex body's projections or sections determine that body. We will see that, if the body is known to be centrally symmetric, then it is determined by the size of its projections. However, without the symmetry condition, knowledge of the average shape of projections or sections often determines the body. Rather surprisingly, the dimension of the projections or sections plays a key role and exceptional cases do occur but appear to...
The distribution of the number of nodes in the relative interior of the typical I-segment in homogeneous planar anisotropic STIT Tessellations
A result about the distribution of the number of nodes in the relative interior of the typical I-segment in homogeneous and isotropic random tessellations stable under iteration (STIT tessellations) is extended to the anisotropic case using recent findings from Schreiber/Thäle, Typical geometry, second-order properties and central limit theory for iteration stable tessellations, arXiv:1001.0990 [math.PR] (2010). Moreover a new expression for the values of this probability distribution is presented...
The distribution of unbounded random sets and the multivalued strong law of large numbers in nonreflexive Banach spaces.
The mean of a maximum likelihood estimator associated with the Brownian bridge.
The Reverse Isoperimetric Problem for Gaussian Measure.
The Thinnest Holding-Lattice of a Set.
Translative integral formulae for convex bodies.
Über die konvexe Hülle von Zufallspunkten in Eibereichen.