Simulation of the typical Poisson–Voronoi–Cox–Voronoi cell

Frank Fleischer, Catherine Gloaguen, Volker Schmidt, Florian Voss
2009 Journal of Statistical Computation and Simulation  
We consider stationary Poisson-Voronoi tessellations (PVT) in the Euclidean plane and study properties of Voronoi tessellations induced by linear Poisson processes on the edges of the PVT. We are especially interested in simulation algorithms for the typical cell. Two different simulation algorithms are introduced. The first algorithm directly simulates the typical cell whereas the second algorithm simulates cells from which distributional properties of the typical cell can be obtained. This
more » ... e obtained. This second algorithm can also be used for simulating the typical cell of other Cox-Voronoi tessellations. The implementation of both algorithms is tested for their correctness using random software tests. Then different cell characteristics are studied by simulation and compared to the typical cell of Poisson-Voronoi tessellations and Cox-Voronoi tessellations based on linear Poisson processes on the lines of Poisson line processes. Our results can be applied for example in the analysis of telecommunication networks and vesicle paths on cytoskeletal networks.
doi:10.1080/00949650802106662 fatcat:olrlb7me4nhjvgxzlm5vhawnsq