Related papers: Refined convergence for the Boolean model
Diffusion models are getting popular in generative image and video synthesis. However, due to the diffusion process, they require a large number of steps to converge. To tackle this issue, in this paper, we propose to perform the diffusion…
In the present work we demonstrate the use of a parcellation free connectivity model based on Poisson point processes. This model produces for each subject a continuous bivariate intensity function that represents for every possible pair of…
The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…
Using a recently developed method to simulate percolation on large clusters of distributed machines [N. R. Moloney and G. Pruessner, Phys. Rev. E 67, 037701 (2003)], we have numerically calculated crossing, spanning and wrapping…
We investigate spatial random graphs defined on the points of a Poisson process in $d$-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the…
Poisson-Boltzmann theory is the cornerstone for soft matter electrostatics. We provide novel exact analytical solutions to this non-linear mean-field approach, for the diffuse layer of ions in the vicinity of a planar or a cylindrical…
This paper proposes a new methodology to perform Bayesian inference for a class of multidimensional Cox processes in which the intensity function is piecewise constant. Poisson processes with piecewise constant intensity functions are…
Stationary Poisson processes of lines in the plane are studied whose directional distributions are concentrated on $k \ge 3$ equally spread directions. The random lines of such processes decompose the plane into a collection of random…
In this article, we obtain, for the total variance distance, the error bounds between Poisson and convolution of power series distributions via Stein's method. This provides a unified approach to many known discrete distributions. Several…
In this paper we study "discrete polynomial blending," a term used to define a certain discretized version of curve blending whereby one approximates from the "sum of tensor product polynomial spaces" over certain grids. Our strategy is to…
A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional real Lie algebra of Hamiltonian vector…
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…
We define a general class of random systems of horizontal and vertical weighted broken lines on the quarter plane whose distribution are proved to be translation invariant. This invariance stems from a reversibility property of the model.…
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.…
We report on the computation of the angle-between-leptons distribution in Drell-Yan processes. More precisely we study the recently introduced variable phi*, which provides us with a more accurate probe of the low Q_T domain of Z boson…
We prove quantitative homogenization results for harmonic functions on supercritical continuum percolation clusters--that is, Poisson point clouds with edges connecting points which are closer than some fixed distance. We show that, on…
We study visibility inside the vacant set of three models in $\mathbb R^d$ with slow decay of spatial correlations: Brownian interlacements, Poisson cylinders and Poisson-Boolean models. Let $Q_x$ be the radius of the largest ball centered…
We study point processes that consist of certain centers of point tuples of an underlying Poisson process. Such processes arise in stochastic geometry in the study of exceedances of various functionals describing geometric properties of the…
We extend the results of Arguin et al and A\"\i{}d\'ekon et al on the convergence of the extremal process of branching Brownian motion by adding an extra dimension that encodes the "location" of the particle in the underlying Galton-Watson…
The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent terms by the accompanying compound Poisson laws may be interpreted as rather sharp quantitative estimates…