Related papers: Second moments related to Poisson hyperplane tesse…

Euler's equations for a two-dimensional system can be written in Hamiltonian form, where the Poisson bracket is the Lie-Poisson bracket associated to the Lie algebra of divergence free vector fields. We show how to derive the Poisson…

Consider $\Xi$ a homogeneous Poisson point process on $\mathbb{R}^d$ ($d\geq 2$) with unit intensity with respect to the Lebesgue measure. For $\varepsilon\geq 0$, we define the Boolean model $\Sigma_{p, \varepsilon}$ as the union of the…

The paper derives the optimal second-order coding rate for the continuous-time Poisson channel. We also obtain bounds on the third-order coding rate. This is the first instance of a second-order result for a continuous-time channel. The…

We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…

We investigate the biased quenched trap model on top of a two-dimensional lattice in the case of diverging expected dwell times. By utilizing the double-subordination approach and calculating the return probability in $2$d, we explicitly…

The points of a moment variety are the vectors of all moments up to some order of a family of probability distributions. We study this variety for mixtures of Gaussians. Following up on Pearson's classical work from 1894, we apply current…

Coupled solitary waves in optics literature, are coined vector solitons to reflect their particle--like nature that remains intact even after mutual collisions. They are born from a nonlinear change in the refractive index of an optical…

Stationary and isotropic iteration stable random tessellations are considered, which can be constructed by a random process of cell division. The collection of maximal polytopes at a fixed time $t$ within a convex window $W\subset{\Bbb…

In the full rectangular version of Gilbert's tessellation lines extend either horizontally (with east- and west--growing rays) or vertically (north- and south--growing rays) from seed points which form a Poisson point process, each ray…

We study random polytopes of the form $[X_1,\ldots,X_n]$ defined as convex hulls of independent and identically distributed random points $X_1,\ldots,X_n$ in $\mathbb{R}^d$ with one of the following densities: $$ f_{d,\beta} (x) =…

Consider a second-order elliptic operator $L$ in the half-plane $\mathbb R \times (0, \infty)$ with coefficients depending only on the second coordinate. The Poisson kernel for $L$ is used in the representation of positive $L$-harmonic…

The Boltzmann equation for $d$-dimensional inelastic Maxwell models is considered to determine the collisional moments of second, third and fourth degree in a granular binary mixture. These collisional moments are exactly evaluated in terms…

The concept of typical and weighted typical spherical faces for tessellations of the $d$-dimensional unit sphere, generated by $n$ independent random great hyperspheres distributed according to a non-degenerate directional distribution, is…

We study the determination of the second-order normal form for perturbed Hamiltonians $H_{\epsilon}=H_0 +\epsilon H_1 +\frac{\epsilon^2}{2} H_2$, relative to the periodic flow of the unperturbed Hamiltonian $H_0$. The formalism presented…

We consider the $d$-neighbor bootstrap percolation process on the $d$-dimensional torus, with vertex set $V=\{1,\cdots,n\}^d$ and edge set $\{xy:\sum_{i=1}^d|x_i-y_i (\text{mod} \; n)|=1\}$. We determine the percolation time up to a…

The purpose of this work is to find the time dependent distributions of directions and positions of a particle that undergoes multiple elastic scattering. The angular cross section is given and the scatterers are randomly placed. The…

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…

In the spherical Poisson Boolean model, one takes the union of random balls centred on the points of a Poisson process in Euclidean $d$-space with $d \geq 2$. We prove that whenever the radius distribution has a finite $d$-th moment, there…

In this paper we study random flights in R^d with displacements possessing Dirichlet distributions of two different types and uniformly oriented. The randomization of the number of displacements has the form of a generalized Poisson process…

Motivated by an application in wireless telecommunication networks, we consider a two-type continuum-percolation problem involving a homogeneous Poisson point process of users and a stationary and ergodic point process of base stations.…