Related papers: Statistical properties of planar Voronoi tessellat…
Voronoi tessellations of Poisson point processes are widely used for modeling many types of physical and biological systems. In this paper, we analyze simulated Poisson-Voronoi structures containing a total of 250,000,000 cells to provide…
High energy experimental data can be viewed as a sampling of the relevant phase space. We point out that one can apply Voronoi tessellations in order to understand the underlying probability distributions in this phase space. Interesting…
In this paper we investigate relationships between the volumes of cells of three-dimensional Voronoi tessellations and the lengths and areas of sections obtained by intersecting the tessellation with a randomly oriented plane. Here, in…
A new class of random spatial tessellations is introduced -- the so-called column tessellations of three-dimensional space. The construction is based on a stationary planar tessellation. Each cell of the spatial tessellation is a prism…
We develop a set of heuristic arguments to explain several results on planar Poisson-Voronoi tessellations that were derived earlier at the cost of considerable mathematical effort. The results concern Voronoi cells having a large number n…
In this brief review, I discuss recent developments in the study of pulsar-powered nebulae ("plerions"). The large volume of data which has been acquired in recent years reveals a diverse range of observational properties, demonstrating how…
Poisson point processes provide a versatile framework for modeling the distributions of random points in space. When the space is partitioned into cells, each associated with a single generating point from the Poisson process, there appears…
Recently, the authors showed that the critical probability for random Voronoi percolation in the plane is 1/2. A by-product of the method was a short proof of the Harris-Kesten Theorem concerning bond percolation in the planar square…
Many physical systems can be studied as collections of particles embedded in space, evolving through deterministic evolution equations. Natural questions arise concerning how to characterize these arrangements - are they ordered or…
We make use of the recent proof that the critical probability for percolation on random Voronoi tessellations is 1/2 to prove the corresponding result for random Johnson-Mehl tessellations, as well as for two-dimensional slices of higher…
In photorealistic image rendering, Monte Carlo methods form the foundation for the integration of the rendering equation in modern approaches. However, despite their effectiveness, traditional Monte Carlo methods often face challenges in…
We introduce a new class of spatial-temporal point processes based on Voronoi tessellations. At each step of such a process, a point is chosen at random according to a distribution determined by the associated Voronoi cells. The point is…
In this paper we show existence of all exponential moments for the total edge length in a unit disk for a family of planar tessellations based on stationary point processes. Apart from classical such tessellations like the Poisson-Voronoi,…
We introduce a dynamical system based on the vertices of Voronoi tessellations. This dynamical system acts on finite or discrete point sets in the plane, taking a point set to the vertex set of its Voronoi tessellation. We explore the…
We prove annealed scaling relations for planar Voronoi percolation. To our knowledge, this is the first result of this kind for a continuum percolation model. We are mostly inspired by the proof of scaling relations for Bernoulli…
A review of some of the recent experimental developments concerning the X, Y and Z charmoniumlike meson states is presented.
The Voronoi tessellation is the partition of space for a given seeds pattern and the result of the partition depends completely on the type of given pattern "random", Poisson-Voronoi tessellations (PVT), or "non-random", Non Poisson-Voronoi…
Spatial statistical analysis of multivariate volumetric data can be challenging due to scale, complexity, and occlusion. Advances in topological segmentation, feature extraction, and statistical summarization have helped overcome the…
Real complex networks are often characterized by spatial constraints such as the relative position and adjacency of nodes. The present work describes how Voronoi tessellations of the space where the network is embedded provide not only a…
Random tessellations are a prominent class of models in stochastic geometry. In this chapter, we give an overview of mechanisms that have been used to formulate random tessellation models. First, the notion of a random tessellation and…