Related papers: Poisson approximation for large-contours in low-te…
We numerically study the finite-size droplet condensation-evaporation transition in two dimensions. We consider and compare two orthogonal approaches, namely at fixed temperature and at fixed density, making use of parallel multicanonical…
This paper establishes quantitative limit theorems for two classes of Cox point processes, quantifying their convergence to a Poisson point process (PPP). We employ Stein's method for PPP aproximation, leveraging the generator approach and…
Motivated by Alain-Sol Sznitman's interlacement process, we consider the set of $\{0,1\}$-valued processes which can be constructed in an analogous way, namely as a union of sets coming from a Poisson process on a collection of sets. Our…
For integer valued random variables, the translated Poisson distributions form a flexible family for approximation in total variation, in much the same way that the normal family is used for approximation in Kolmogorov distance. Using the…
Simulation of human soft tissues in contact with their environment is essential in many fields, including visual effects and apparel design. Biological tissues are nearly incompressible. However, standard methods employ compressible…
From the microscopic theory, we derive a number conserving quantum kinetic equation, valid for a dilute Bose gas at any temperature, in which the binary collisions between the quasi-particles are mediated by phonon-like excitations (called…
Let $X_1,\ldots,X_n$ be a sequence of independent random points in $\mathbb{R}^d$ with common Lebesgue density $f$. Under some conditions on $f$, we obtain a Poisson limit theorem, as $n \to \infty$, for the number of large probability…
Peccati, Sole, Taqqu, and Utzet recently combined Stein's method and Malliavin calculus to obtain a bound for the Wasserstein distance of a Poisson functional and a Gaussian random variable. Convergence in the Wasserstein distance always…
In this paper we report simulation studies of equilibrium features, namely circular islands on model surfaces, using Monte-Carlo methods. In particular, we are interested in studying the relationship between the density of vapour around a…
We study a system of penetrable bosons on a line, focusing on the high-density/weak-interaction regime, where the ground state is, to a good approximation, a condensate. Under compression, the system clusterizes at zero temperature, i.e.,…
Consider a pair of input distributions which after passing through a Poisson channel become $\epsilon$-close in total variation. We show that they must necessarily then be $\epsilon^{0.5+o(1)}$-close after passing through a Gaussian channel…
We develop a new method that allows us to map models of interacting fermions onto bosonic models describing collective excitations in an arbitrary dimension. This mapping becomes exact in the thermodynamic continuous time limit. The boson…
Based on Stein's method, we derive upper bounds for Poisson process approximation in the $L_1$-Wasserstein metric $d_2^{(p)}$, which is based on a slightly adapted $L_p$-Wasserstein metric between point measures. For the case $p=1$, this…
The framework of Stein's method for Poisson process approximation is presented from the point of view of Palm theory, which is used to construct Stein identities and define local dependence. A general result (Theorem…
In this paper, we give an upper bound for a probabilistic distance between a Gaussian vector and a vector of U-statistics of Poisson point processes by applying Malliavin-Stein inequality on the Poisson space.
Let $X$ be a Poisson point process and $K\subset\mathbb{R}^d$ a measurable set. Construct the Voronoi cells of all points $x\in X$ with respect to $X$, and denote by $v_X(K)$ the union of all Voronoi cells with nucleus in $K$. For $K$ a…
The realization of Bose-Einstein condensation in ultracold trapped gases has led to a revival of interest in that fascinating quantum phenomenon. This experimental achievement necessitated both extremely low temperatures and sufficiently…
The paper is concerned with the equilibrium distributions of continuous-time density dependent Markov processes on the integers. These distributions are known typically to be approximately normal, and the approximation error, as measured in…
Ground states and dynamical properties of dipolar Bose-Einstein condensate are analyzed based on the Gross-Pitaevskii-Poisson system (GPPS) and its dimension reduction models under anisotropic confining potential. We begin with the…
We study a local thinning $T_r$ that retains a point with probability $p(n_r)$, where $n_r$ counts neighbors within radius $r$. For Poisson input with spatially varying intensity, we obtain an exact intensity via a Poisson--mixture formula…