Related papers: Full and Half Gilbert Tessellations with Rectangul…
Since the seminal work of Mecke, Nagel and Weiss, the iteration stable (STIT) tessellations have attracted considerable interest in stochastic geometry as a natural and flexible yet analytically tractable model for hierarchical spatial…
We studied the complete randomness of the angular distribution of gamma-ray bursts (GRBs) detected by BATSE. Since GRBs seem to be a mixture of objects of different physical nature we divided the BATSE sample into 5 subsamples (short1,…
A Poisson line tessellation is observed within a window. With each cell of the tessellation, we associate the inradius, which is the radius of the largest ball contained in the cell. Using Poisson approximation, we compute the limit…
A stationary Poisson line tessellation is considered whose directional distribution is concentrated on two different atoms with some positive weights. The shape of the typical cell of such a tessellation is studied when its area or its…
Poisson Voronoi tessellations have been used in modeling many types of systems across different sciences, from geography and astronomy to telecommunications. The existing literature on the statistical properties of Poisson Voronoi cells is…
Processes of random tessellations of the Euclidean space $\mathbb{R}^d$, $d\geq 1$, are considered which are generated by subsequent division of their cells. Such processes are characterized by the laws of the life times of the cells until…
Precise modeling of extended sources is a central challenge in modern optical engineering, laser physics, and computational lithography. Unlike ideal point sources or completely incoherent thermal radiation sources, real-world light sources…
Until now, little was known about properties of small cells in a Poisson hyperplane tessellation. The few existing results were either heuristic or applying only to the two dimensional case and for very specific size functionals and…
Angle halving, or alternatively the reverse operation of angle doubling, is a useful tool when studying directional distributions. It is especially useful on the circle where, in particular, it yields an identification between the wrapped…
Recent experiments revealed that the dielectric dispersion spectrum of fission yeast cells in a suspension was mainly composed of two sub-dispersions. The low-frequency sub-dispersion depended on the cell length, whereas the high-frequency…
A rigorous methodology is proposed to study cell division data consisting in several observed genealogical trees of possibly different shapes. The procedure takes into account missing observations, data from different trees, as well as the…
While analyzing mobile systems we often approximate the actual coverage surface and assume an ideal cell shape. In a multi-cellular network, because of its tessellating nature, a hexagon is more preferred than a circular geometry. Despite…
We pursue two goals in this article. As our first goal, we construct a family $\mathcal{M}_G$ of Gibbs like measures on the set of piecewise linear convex functions $g:\mathbb{R}^2\to\mathbb{R}$. It turns out that there is a one-to-one…
We show that radiation from complex and inherently random but correlated wave sources can be modelled efficiently by using an approach based on the Wigner distribution function. Our method exploits the connection between correlation…
Arising as a fluctuation phenomenon, the equilibrium distribution of meandering steps with mean separation $<\ell>$ on a "tilted" surface can be fruitfully analyzed using results from RMT. The set of step configurations in 2D can be mapped…
We focus on the distribution regression problem: regressing to a real-valued response from a probability distribution. Although there exist a large number of similarity measures between distributions, very little is known about their…
We study the distribution regression problem assuming the distribution of distributions has a doubling measure larger than one. First, we explore the geometry of any distributions that has doubling measure larger than one and build a small…
We consider Gaussian approximation in three particular models of Poisson-Laguerre tessellations, namely, the $\beta$-, $\beta'$- and Gaussian-Voronoi tessellations. The tessellations are constructed based on inhomogeneous Poisson point…
Standard Gibbs sampling applied to a multivariate normal distribution with a specified precision matrix is equivalent in fundamental ways to the Gauss-Seidel iterative solution of linear equations in the precision matrix. Specifically, the…
A method is developed to compute the chord length distribution along a line which intersects a cellular Universe. The cellular Universe is here modeled by the Poissonian Voronoi Tessellation (PVT) and by a non-Poissonian Voronoi…