We consider two stochastic processes, the Gribov process and the general epidemic process, that describe the spreading of an infectious disease. In contrast to the usually assumed case of shortrangeâ€¦ (More)

In planar cellular systems mn denotes the average sidedness of a cell neighboring an n-sided cell. Aboavâ€™s empirical law states that nmn is linear in n. A downward curvature is nevertheless observedâ€¦ (More)

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 resultsâ€¦ (More)

The sum of N sufficiently strongly correlated random variables will not in general be Gaussian distributed in the limit N â†’ âˆž. We revisit examples of sums x that have recently been put forward asâ€¦ (More)

We achieve a detailed understanding of the n-sided planar PoissonVoronoi cell in the limit of large n. Let pn be the probability for a cell to have n sides. We construct the asymptotic expansion ofâ€¦ (More)

We present the first example of a phase transition in a nonequi libri m steady-state that can be argued analytically to be first order. The system of intere st is a two-species reactionâ€“ diffusionâ€¦ (More)

By a new Monte Carlo algorithm we evaluate the sidedness probability pn of a planar Poisson-Voronoi cell in the range 3 â‰¤ n â‰¤ 1600. The algorithm is developed on the basis of earlier theoreticalâ€¦ (More)

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 parameterâ€¦ (More)

We consider the d-dimensional Poisson-Voronoi tessellation and investigate the applicability of heuristic methods developed recently for two dimensions. Let pn(d) be the probability that a cell haveâ€¦ (More)