Random affine simplexes

Counting Simplexes in R

A finite set of vectors S ⊆ R is called a simplex iff S is linearly dependent but all its proper subsets are independent. This concept arises in particular from stoichiometry. We are interested in this paper in the number of simplexes contained in some H ⊆ R , which we denote by simp(H). This investigation is particularly interesting for H spanning R and containing no collinear vectors. Our mai...

Counting Simplexes in R3

A nite set of vectors S R n is called a simplex ii S is linearly dependent but all its proper subsets are independent. This concept arises in particular from stoichiometry. We are interested in this paper in the number of simplexes contained in

Delaunay simplexes in physics

Delaunay simplexes are very helpful instrument for analysis of computer models of atomic, molecular and granular systems. This paper illustrates their application to the current physical problems. The first one is the structure of non-crystalline packing of spheres. Recently it got the advance thanks to application of the Delaunay simplexes with quantitative measures of simplex shape. The secon...

Random Distributions, Random Affine Systems, Sampling of Renewal Processes

Isotropic Random Walks on Affine Buildings

Recently, Cartwright and Woess [5] provided a detailed analysis of isotropic random walks on the vertices of thick affine buildings of type Ãn. Their results generalise results of Sawyer [18] where homogeneous trees are studied (these are Ã1 buildings), and Lindlbauer and Voit [9], where Ã2 buildings are studied. In this paper we apply techniques of spherical harmonic analysis to prove a local ...