Related papers: Statistical properties of planar Voronoi tessellat…
In these notes we review recent progress (and, in Section \ref{sec:ados}, we announce a new result) concerning the statistical properties of the spectrum of Wigner random matrices.
A survey is given on the present knowledge of the polarized parton distribution functions. We give an outlook for further developments desired both on the theoretical as well on the experimental side to complete the understanding of the…
General models of Gibbs Delaunay-Voronoi tessellations, which can be viewed as extensions of Ord's process, are considered. The interaction may occur on each cell of the tessellation and between neighbour cells. The tessellation may also be…
Poisson Voronoi tessellations have been used in modeling many types of systems across different sciences, from geography and astronomy to telecommunications. The existing literature on the statistical properties of Poisson Voronoi cells is…
Since the seminal work by Nagel and Weiss, the iteration stable (STIT) tessellations have attracted considerable interest in stochastic geometry as a natural and flexible, yet analytically tractable model for hierarchical spatial…
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 introduce two new methods to obtain reliable velocity field statistics from N-body simulations, or indeed from any general density and velocity fluctuation field sampled by discrete points. These methods, the {\it Voronoi tessellation…
The purpose of this review paper is to summarise the pulsar timing method, to provide an overview of recent research into the spin-down of pulsars over decadal timescales and to highlight the science that can be achieved using…
We present a survey on recent developments of generalizations of Forelli's analyticity theorem and related pluripotential methods.
We give a brief overview on some of the latest results on the transversity function. We focus on some recent extractions from azimuthal asymmetries data measured in semi-inclusive deep-inelastic scattering processes, and on the impact of…
We survey recent results on Calderon's inverse problem with partial data, focusing on three and higher dimensions.
Consider a homogeneous Poisson point process of the Euclidean plane and its Voronoi tessellation. The present note discusses the properties of two stationary point processes associated with the latter and depending on a parameter $\theta$.…
The computation of Voronoi Diagrams, or their dual Delauney triangulations is difficult in high dimensions. In a recent publication Polianskii and Pokorny propose an iterative randomized algorithm facilitating the approximation of Voronoi…
In this study the Voronoi interpolation is used to interpolate a set of points drawn from a topological space with higher homology groups on its filtration. The technique is based on Voronoi tessellation, which induces a natural dual map to…
We herein review the recent progress on the study of metastability based on the analysis of solutions of Poisson equations related to the generators of the underlying metastable dynamics. This review paper is based on the joint work with…
The large-scale matter distribution represents a complex network of structure elements such as voids, clusters, filaments, and sheets. This network is spanned by a point distribution. The global properties of the point process can be…
Owing to the natural interpretation and various desirable mathematical properties, centroidal Voronoi tessellations (CVT) have found a wide range of applications and correspondingly a vast development in their literature. However the…
We present a novel analysis method for measurements of polarization transferred in $A(\vec{e},e'\vec{N})$ experiments, which can be applied to other kinds of polarization measurements as well. In this method the polarization transfer…
In this paper, we introduce two identities one pertaining to the state space of Poisson Point Processes (PPPs), and the other for the Voronoi tessellations formed by PPPs. Then, we explore several applications of these identities within the…
Asteroseismology provides us with a unique opportunity to improve our understanding of stellar structure and evolution. Recent developments, including the first systematic studies of solar-like pulsators, have boosted the impact of this…