Related papers: The Moment Generating function for ray lengths in …
We investigate the ray-length distributions for two different rectangular versions of Gilbert's tessellation. In the full rectangular version, lines extend either horizontally (with east- and west-growing rays) or vertically (north- and…
A random planar quadrangulation process is introduced as an approximation for certain cellular automata in terms of random growth of rays from a given set of points. This model turns out to be a particular (rectangular) case of the…
A Gilbert tessellation arises by letting linear segments (cracks) in the plane unfold in time with constant speed, starting from a homogeneous Poisson point process of germs in randomly chosen directions. Whenever a growing edge hits an…
The formalism devoted to the production of two pseudoscalar mesons with a linearly polarized photon beam has been detailed and illustrated in Phys. Rev. D100 (2019) 054017. This document reports the necessary formulas, without proof, to…
For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour of the resulting random graph, the Gilbert graph or random…
We calculate moments and moment generating functions of two distributions: the so called $q-$Normal and the so called conditional $q-$Normal distributions. These distributions generalize both Normal ($q=1),$ Wigner ($% q=0,$ $q-$Normal) and…
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…
We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the…
We present a convenient method to generate vector beams of light having polarization singularities on their axis, via partial spin-to-orbital angular momentum conversion in a suitably patterned liquid crystal cell. The resulting…
We consider the typical cell of a stationary Poisson hyperplane tessellation in d-dimensional Euclidean space. It is well known that the expected vertex number of the typical cell is independent of the directional distribution of the…
We consider the time evolution of the supercritical Galton-Watson model of branching particles with extra parameter (mass). In the moment of the division the mass of the particle (which is growing linearly after the birth) is divided in…
We apply the Golec-Biernat Wuesthoff model in the calculation of vector meson photo- and electroproduction. Starting from very simple non-relativistic wave functions we show that the model provides a good description of $J/\Psi$ cross…
We study semi-martingale obliquely reflected Brownian motion with drift in the first quadrant of the plane in the transient case. Our main result determines a general explicit integral expression for the moment generating function of…
A rectangular dual of a graph $G$ is a contact representation of $G$ by axis-aligned rectangles such that (i)~no four rectangles share a point and (ii)~the union of all rectangles is a rectangle. The partial representation extension problem…
For cell-division processes in a window, Cowan introduced four selection rules and two division rules each of which stands for one cell-division model. One of these is the area-weighted in-cell model. In this model, each cell is selected…
The point process of vertices of an iteration infinitely divisible or more specifically of an iteration stable random tessellation in the Euclidean plane is considered. We explicitly determine its covariance measure and its pair-correlation…
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…
We present the exact solution to the moment problem for the spin-1/2 isotropic antiferromagnetic XY chain with explicit forms for the moments with respect to the Neel state, the cumulant generating function, and the Resolvent Operator. We…
We investigate properties of the particle distribution near the tip of one-dimensional branching random walks at large times $t$, focusing on unusual realizations in which the rightmost lead particle is very far ahead of its expected…
We study branching processes of independently splitting particles in the continuous time setting. If time is calibrated such that particles live on average one unit of time, the corresponding transition rates are fully determined by the…