Related papers: Poisson polyhedra in high dimensions

We prove that by scaling nearest-neighbour ferromagnetic energies defined on Poisson random sets in the plane we obtain an isotropic perimeter energy with a surface tension characterised by an asymptotic formula. The result relies on…

We study a coarsening process of one-dimensional cell complexes. We show that if cell boundaries move with velocities proportional to the difference in size of neighboring cells, then the average cell size grows at a prescribed exponential…

This paper studied the fundamental modeling defect existing in Poisson-distributed cellular networks in which all base stations form a homogeneous Poisson point process (PPP) of intensity $\lambda_B$ and all users form another independent…

Consider a planar random point process made of the union of a point (the origin) and of a Poisson point process with a uniform intensity outside a deterministic set surrounding the origin. When the intensity goes to infinity, we show that…

We study the asymptotic behavior of a size-marked point process of centers of large cells in a stationary and isotropic Poisson hyperplane mosaic in dimension $d \ge 2$. The sizes of the cells are measured by their inradius or their $k$th…

Suppose that $Z$ is a random closed subset of the hyperbolic plane $\H^2$, whose law is invariant under isometries of $\H^2$. We prove that if the probability that $Z$ contains a fixed ball of radius 1 is larger than some universal constant…

The action of the Cremona group of rank 2 on an infinite dimensional hyperbolic space is the main recent tool to study the Cremona group. Following the analogy with the action of PSL(2,Z) on the Poincar\'e half-plane, we exhibit a…

The Voronoi tessellation is the partition of space for a given seeds pattern and the result of the partition depends completely on the type of given pattern "random", Poisson-Voronoi tessellations (PVT), or "non-random", Non Poisson-Voronoi…

Let Z be a so-called well-behaved percolation, i.e. a certain random closed set in the hyperbolic plane, whose law is invariant under all isometries; for example the covered region in a Poisson Boolean model. The Hausdorff-dimension of the…

In a previous work, two of the authors proposed a new proof of a well known convergence result for the scaled elementary connected vacant component in the high intensity Boolean model towards the Crofton cell of the Poisson hyperplane…

A homogeneous Poisson-Voronoi tessellation of intensity $\gamma$ is observed in a convex body $W$. We associate to each cell of the tessellation two characteristic radii: the inradius, i.e. the radius of the largest ball centered at the…

We study Poisson traces of the structure algebra A of an affine Poisson variety X defined over a field of characteristic p. According to arXiv:0908.3868v4, the dual space HP_0(A) to the space of Poisson traces arises as the space of…

We achieve a detailed understanding of the $n$-sided planar Poisson-Voronoi cell in the limit of large $n$. Let ${p}\_n$ be the probability for a cell to have $n$ sides. We construct the asymptotic expansion of $\log {p}\_n$ up to terms…

This paper establishes expectation and variance asymptotics for statistics of the Poisson--Voronoi approximation of general sets, as the underlying intensity of the Poisson point process tends to infinity. Statistics of interest include…

By a new Monte Carlo algorithm we evaluate the sidedness probability p_n of a planar Poisson-Voronoi cell in the range 3 \leq n \leq 1600. The algorithm is developed on the basis of earlier theoretical work; it exploits, in particular, the…

The cell-model and its treatment on the Poisson-Boltzmann level are two important concepts in the theoretical description of charged macromolecules. In this brief contribution to the Proceedings of the NATO-ASI on ``Electrostatic Effects in…

Motivated by problems of hyperbolic stochastic geometry we introduce and study the class of beta-star polytopes. A beta-star polytope is defined as the convex hull of an inhomogeneous Poisson processes on the complement of the unit ball in…

At each point of a Poisson point process of intensity $\lambda$ in the hyperbolic place, center a ball of bounded random radius. Consider the probability $P_r$ that from a fixed point, there is some direction in which one can reach distance…

We consider the Voronoi tessellation based on a homogeneous Poisson point process in $\mathbf{R}^{d}$. For a geometric characteristic of the cells (e.g. the inradius, the circumradius, the volume), we investigate the point process of the…

We study an inhomogeneous random connection model in the connectivity regime. The vertex set of the graph is a homogeneous Poisson point process $\mathcal{P}_s$ of intensity $s>0$ on the unit cube…