相关论文: Many-faced cells and many-edged faces in 3D Poisso…

Two models of random cones in high dimensions are considered, together with their duals. The Donoho-Tanner random cone $D_{n,d}$ can be defined as the positive hull of $n$ independent $d$-dimensional Gaussian random vectors. The Cover-Efron…

We stress the importance of stochastic geometry as a branch of mathematical statistics particularly suited to model and investigate nontrivial spatial patterns. One of its key concepts, Voronoi tessellations, represents a versatile and…

Stereology allows shifting from the 3D distribution of the volumes of Poissonian Voronoi Diagrams to their 2D cross-sections. The basic assumption is that the 3D statistics of the volumes of the voids in the local Universe has a…

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 suggest a new hardcore Poisson-type distribution for Young diagrams with the row lengths from some finite list. A discrete variant of the time-ordered Mat\'{e}rn II process in 1D is employed. This approach is related to that based on the…

We study the asymptotic behavior of solutions to the Vlasov equation in the presence of a strong external magnetic field. In particular we provide a mathematically rigorous derivation of the guiding-center approximation in the general three…

We consider the adjacency matrix $A$ of the Erd\H{o}s-R\'enyi graph on $N$ vertices with edge probability $d/N$. For $(\log \log N)^4 \ll d \lesssim \log N$, we prove that the eigenvalues near the spectral edge form asymptotically a Poisson…

We consider the Poisson-Boltzmann equation in a periodic cell, representative of a porous medium. It is a model for the electrostatic distribution of $N$ chemical species diluted in a liquid at rest, occupying the pore space with charged…

To every Poisson algebraic variety X over an algebraically closed field of characteristic zero, we canonically attach a right D-module M(X) on X. If X is affine, solutions of M(X) in the space of algebraic distributions on X are Poisson…

Given a network, the statistical ensemble of its graph-Voronoi diagrams with randomly chosen cell centers exhibits properties convertible into information on the network's large scale structures. We define a node-pair level measure called…

In a convex mosaic in $\mathbb{R} ^d$ we denote the average number of vertices of a cell by $\bar v$ and the average number of cells meeting at a node by $\bar n$. Except for the $d=2$ planar case, there is no known formula prohibiting…

Vershik and Kerov gave asymptotical bounds for the maximal and the typical dimensions of irreducible representations of symmetric groups $S_n$. It was conjectured by G. Olshanski that the maximal and the typical dimensions of the isotypic…

We show that a realization of a closed connected PL-manifold of dimension n-1 in Euclidean n-space (n>2) is the boundary of a convex polyhedron if and only if the interior of each (n-3)-face has a point, which has a neighborhood lying on…

Computational technologies for the approximate solution of multidimensional boundary value problems often rely on irregular computational meshes and finite-volume approximations. In this framework, the discrete problem represents the…

Fix $d \ge 3$. We show the existence of a constant $c>0$ such that any graph of diameter at most $d$ has average distance at most $d-c \frac{d^{3/2}}{\sqrt n}$, where $n$ is the number of vertices. Moreover, we exhibit graphs certifying…

Random tessellations of the space represent a class of prototype models of heterogeneous media, which are central in several applications in physics, engineering and life sciences. In this work, we investigate the statistical properties of…

We derive a formula expressing the average number $E_n$ of real lines on a random hypersurface of degree $2n-3$ in $\mathbb{R}\textrm{P}^n$ in terms of the expected modulus of the determinant of a special random matrix. In the case $n=3$ we…

We impose the uniform probability measure on the set of all discrete Gelfand-Tsetlin patterns of depth $n$ with the particles on row $n$ in deterministic positions. These systems equivalently describe a broad class of random tilings models,…

For sequences of Poisson-Laguerre tessellations and their duals in $\mathbb{R}^d$, generated by Poisson point processes $(\eta_n)_{n\in\mathbb{N}}$ in $\mathbb{R}^d \times \mathbb{R}$, we prove limit theorems as $n\to \infty$. The intensity…

Considering regions in a map to be adjacent when they have nonempty intersection (as opposed to the traditional view requiring intersection in a linear segment) leads to the concept of a facially complete graph: a plane graph that becomes…