Related papers: Cells with many facets in a Poisson hyperplane tes…

We show that a compound Poisson distribution holds for scaled exceedances of observables $\phi$ uniquely maximized at a periodic point $\zeta$ in a variety of two-dimensional hyperbolic dynamical systems with singularities $(M,T,\mu)$,…

Layered superconductors like High-Tc cuprates display out-of-plane plasma oscillations between layers sustained by the weak Josephson coupling among the superconducting sheets, the so-called Josephson plasmons. Bilayer cuprates hosts two of…

We bridge the properties of the regular square and honeycomb Voronoi tessellations of the plane to those of the Poisson-Voronoi case, thus analyzing in a common framework symmetry-break processes and the approach to uniformly random…

While analyzing mobile systems we often approximate the actual coverage surface and assume an ideal cell shape. In a multi-cellular network, because of its tessellating nature, a hexagon is more preferred than a circular geometry. Despite…

We consider the statistical properties of the gravitational field F in an infinite one-dimensional homogeneous Poisson distribution of particles, using an exponential cut-off of the pair interaction to control and study the divergences…

For each pair $(Q_i,Q_j)$ of reference points and each real number $r$ there is a unique hyperplane $h \perp Q_iQ_j$ such that $d(P,Q_i)^2 - d(P,Q_j)^2 = r$ for points $P$ in $h$. Take $n$ reference points in $d$-space and for each pair…

We study the concentration of the norm of a random vector $Y$ uniformly sampled in the centered zero cell of two types of stationary and isotropic random mosaics in $\mathbb{R}^n$ for large dimensions $n$. For a stationary and isotropic…

We are interested in the distribution of the number of faces across all the $2-$cell embeddings of a graph, which is equivalent to the distribution of genus by Euler's formula. In order to study this distribution, we consider the local…

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…

By the method of Poissonization we confirm some existing results concerning consistent estimation of the structural distribution function in the situation of a large number of rare events. Inconsistency of the so called natural estimator is…

Let K be a d-dimensional convex body, and let $K^{(n)}$ be the intersection of n halfspaces containing $K$ whose bounding hyperplanes are independent and identically distributed. Under suitable distributional assumptions, we prove an…

We present a model calculation of the generalized parton distributions where the nucleon is described by a quark core surrounded by a mesonic cloud. In the one-meson approximation, we expand the Fock state of the physical nucleon in a…

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…

Voronoi tessellations of scale-invariant fractal sets are characterized by topological and metrical properties that are significantly different from those of natural cellular structures. As an example we analyze Voronoi diagrams of…

Let $\Xi_n=\{\xi_1,\dots,\xi_n\}$ be a sample of $n$ independent points distributed in a regular closed element $K$ of the extended convex ring in $\mathbb{R}^d$ according to a probability measure $\mu$ on $K$, admitting a density function.…

From solar supergranulation to salt flat in Bolivia, from veins on leaves to cells on Drosophila wing discs, polygon-based networks exhibit great complexities, yet similarities persist and statistical distributions can be remarkably…

Realistic charged macromolecules are characterized by discrete (rather than homogeneous) charge distributions. We investigate the effects of surface charge discretization on the counterion distribution at the level of mean-field theory…

Pick $d+1$ points uniformly at random on the unit sphere in $\mathbb R^d$. What is the expected value of the angle sum of the simplex spanned by these points? Choose $n$ points uniformly at random in the $d$-dimensional ball. What is the…

A tessellation of the plane is face-homogeneous if for some integer $k\geq3$ there exists a cyclic sequence $\sigma=[p_0,p_1,\ldots,p_{k-1}]$ of integers $\geq3$ such that, for every face $f$ of the tessellation, the valences of the…

We consider the distribution of spacings between consecutive elements in subsets of Z/qZ where q is highly composite and the subsets are defined via the Chinese remainder theorem. We give a sufficient criterion for the spacing distribution…