Related papers: Intersection and proximity of processes of flats
The aim of this paper is two-fold. First we analyze the sequence of intensity measures of a spatial branching point process arising in a multiple target tracking context. We study its stability properties, characterize its long time…
We prove a Poisson process approximation result for stabilizing functionals of a determinantal point process. Our results use concrete couplings of determinantal processes with different Palm measures and exploit their association…
Operators, refered to as k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of two noncommuting quon algebras. The deformation parameters for these quon algebras are roots of…
In the present paper we give a brief summary of some recent theoretical advances in the treatment of inhomogeneous fluids and methods which have applications in the study of dynamical properties of liquids in situations of extreme…
We introduce a novel approach for studying random k-coverage, using Morse theory for the k-nearest neighbor (k-NN) distance function. We prove a sharp phase transition for the number of critical points of the k-NN distance function, from…
The statistical-mechanical study of the equilibrium properties of fluids, starting from the knowledge of the interparticle interaction potential, is essential to understand the role that microscopic interaction between individual particles…
Under explicit diophantine conditions on $(\alpha,\beta)\in\RR^2$, we prove that the local two-point correlations of the sequence given by the values $(m-\alpha)^2+\break (n-\beta)^2$, with $(m,n)\in\ZZ^2$, are those of a Poisson process.…
Given a stationary and isotropic Poisson hyperplane process and a convex body $K$ in ${\mathbb R}^d$, we consider the random polytope defined by the intersection of all closed halfspaces containing $K$ that are bounded by hyperplanes of the…
Totally asymmetric simple exclusion processes (TASEP) with particles which occupy more than one lattice site and with a local inhomogeneity far away from the boundaries are investigated. These non-equilibrium processes are relevant for the…
Many practical approximations in physics and engineering invoke a relatively long physical domain with a relatively thin cross-section. In this scenario we typically expect the system to have structures that vary slowly in the long…
This article employs the relation between probabilities of two consecutive values of a Poisson random variable to derive conditions for the weak convergence of point processes to a Poisson process. As applications, we consider the starting…
We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics like the F function. For pairwise interaction processes we…
We consider a general class of statistical experiments, in which an $n$-dimensional centered Gaussian random variable is observed and its covariance matrix is the parameter of interest. The covariance matrix is assumed to be…
This paper deals with feature selection procedures for spatial point processes intensity estimation. We consider regularized versions of estimating equations based on Campbell theorem derived from two classical functions: Poisson likelihood…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
In this doctoral thesis we have studied the quantum properties of several models which have been classified as statical and dynamical systems. The first part has been devoted to investigate the properties of the statical models including…
Atomic reconstruction in twisted transition metal dichalcogenide heterostructures leads to mesoscopic domains with uniform atomic registry, profoundly altering the local potential landscape. While interlayer excitons in these domains…
We develop Green's function formalism to describe continuous multi-layered quasi-one-dimensional setups described by piece-wise constant single-particle Hamiltonians. The Hamiltonians of the individual layers are assumed to be quadratic…
We restrict our attention to space-time point pattern data for which we have a single realisation within a finite region. Second-order characteristics are used to analyse the spatio-temporal structure of the underlying point process. In…
This paper introduces a new asymptotic regime for simplifying stochastic models having non-stationary effects, such as those that arise in the presence of time-of-day effects. This regime describes an operating environment within which the…