Related papers: Two identities for Poisson Point Processes and Vor…
The voids between galaxies are identified with the volumes of the Poisson Voronoi tessellation. Two new survival functions for the apparent radii of voids are derived. The sectional normalized area of the Poisson Voronoi tessellation is…
In field theories one often works with the functionals which are integrals of some densities. These densities are defined up to divergence terms (boundary terms). A Poisson bracket of two functionals is also a functional, i.e., an integral…
In the focus of our attention is the asymptotic properties of the sequence of convex hulls which arise as a result of a peeling procedure applied to the convex hull generated by a Poisson point process. Processes of the considered type are…
We study a cooperation model where the positions of base stations follow a Poisson point process distribution and where Voronoi cells define the planar areas associated with them. For the service of each user, either one or two base…
We provide a description of virtual non-local matrix product operator (MPO) symmetries in projected entangled pair state (PEPS) representations of string-net models. Given such a PEPS representation, we show that the consistency conditions…
In this paper, we consider device-to-device (D2D) communications as an underlay to the cellular networks over both licensed and unlicensed spectrum, where Long Term Evolution (LTE) users utilize the spectrum orthogonally while D2D users…
In our recent paper [de Lacy Costello et al. 2010] we described the formation of complex tessellations of the plane arising from the various reactions of metal salts with potassium ferricyanide and ferrocyanide loaded gels. In addition to…
We introduce a model for the spatial distribution of cell phone antennas in a urban environment. After showing that the complete spatial randomness (homogeneous Poisson distribution) hypothesis does not hold, we propose a model in which…
Consider the distances $\tilde{R}_o$ and $R_o$ from the nucleus to a uniformly random point in the 0-cell and the typical cell, respectively, of the $d$-dimensional Poisson-Voronoi (PV) tessellation. The main objective of this paper is to…
We consider a family of random line tessellations of the Euclidean plane introduced in a much more formal context by Hug and Schneider [Geom. Funct. Anal. 17, 156 (2007)] and described by a parameter \alpha\geq 1. For \alpha=1 the zero-cell…
Poisson-Poisson cluster processes (PPCPs) are a class of point processes exhibiting attractive point patterns. Recently, PPCPs are actively studied for modeling and analysis of heterogeneous cellular networks or device-to-device networks.…
Switching identities have a long history in potential theory and stochastic analysis. In recent work of Cox and Wang, a switching identity was used to connect an optimal stopping problem and the Skorokhod embedding problem (SEP). Typically…
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…
Spatial Poisson point processes on finite-dimensional Euclidean space provide fundamental mathematical tools for modeling random spatial point patterns. In this paper, we introduce and analyze several Poisson-type spatial point processes.…
Networks play a central role in modern data analysis, enabling us to reason about systems by studying the relationships between their parts. Most often in network analysis, the edges are given. However, in many systems it is difficult or…
This study proposes a novel stochastic geometry framework analyzing power control strategies in spatially correlated network topologies. Heterogeneous networks are studied, with users modeled via the superposition of homogeneous and Poisson…
Modelling, specifying and reasoning about complex systems requires to process in an integrated fashion declarative and procedural aspects of the target domain. The paper reports on an experiment conducted with a propositional version of…
We establish the existence of stationary Gibbsian point processes for interactions that act on hyperedges between the points. For example, such interactions can depend on Delaunay edges or triangles, cliques of Voronoi cells or clusters of…
Characterizing the spacing of primary dendrite arms in directionally-solidified microstructures is an important step for developing process-structure-property relationships by enabling the quantification of (i) the influence of processing…
One of the principal underlying assumptions of current approaches to the analysis of heterogeneous cellular networks (HetNets) with random spatial models is the uniform distribution of users independent of the base station (BS) locations.…