Related papers: Refined convergence for the Boolean model
The aim of this paper is to analyze a class of random motions which models the motion of a particle on the real line with random velocity and subject to the action of the friction. The speed randomly changes when a Poissonian event occurs.…
We prove that under an easily verifiable set of conditions a sequence of associated random fields converges under rescaling to the Poisson Point Process and give a couple of examples.
We introduce the Poisson-Boltzmann cell model for spherical colloidal particles with a heterogeneous surface charge distribution. This model is obtained by generalizing existing cell models for mixtures of homogeneously charged colloidal…
We study systems of simple point processes that admit stochastic intensities. We represent these point processes as thinnings of Poisson measures and are interested in a convergence result of such systems. This result states that, if the…
As a first step toward a characterization of the limiting extremal process of branching Brownian motion, we proved in a recent work [Comm. Pure Appl. Math. 64 (2011) 1647-1676] that, in the limit of large time $t$, extremal particles…
We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is…
Plant differently colored points in the plane, then let random points ("Poisson rain") fall, and give each new point the color of the nearest existing point. Previous investigation and simulations strongly suggest that the colored regions…
Accurate and sensitive measurements of higher order cumulants open up new approaches to pion interferometry. It is now possible to test whether a given theoretical prediction can consistently match cumulants of both second and third order.…
We establish a complete picture of condensation in the inclusion process in the thermodynamic limit with vanishing diffusion, covering all scaling regimes of the diffusion parameter and including large deviation results for the maximum…
Randomly diluted quantum boson and spin models in two dimensions combine the physics of classical percolation with the well-known dimensionality dependence of ordering in quantum lattice models. This combination is rather subtle for models…
Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…
This paper develops the large deviations theory for the point process associated with the Euclidean volume of $k$-nearest neighbor balls centered around the points of a homogeneous Poisson or a binomial point processes in the unit cube. Two…
We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so that in particular the motion can be space-inhomogeneous, interacting via one-sided reflections. The prototypical example is the well-known model…
We consider two independent Gaussian processes that admit a representation in terms of a stochastic integral of a deterministic kernel with respect to a standard Wiener process. In this paper we construct two families of processes, from a…
We consider a large class of bullet models that contains, in particular, the colliding bullet model with creations and a new loop model. For this large class of bullet models, we give sufficient conditions on their parameter to be…
The binomial, the negative binomial, the Poisson, the compound Poisson and the Erlang distribution do all admit integral representations with respect to its (continuous) parameter. We use the Margulis-Russo type formulas for Bernoulli and…
We study an inhomogeneous random connection model in the connectivity regime. The vertex set of the graph is a homogeneous Poisson point process $\mathcal{P}_s$ of intensity $s>0$ on the unit cube…
We consider a generalization of the weighted random ball model. The model is driven by a random Poisson measure with a product heavy tailed intensity measure. Such a model typically represents the transmission of a network of stations with…
This note answers one question in [math.PR/0505668], concerning the connected allocation for the Poisson process in R^2. The proposed solution makes use of the Riemann map from the plane minus the minimal spanning forest of the Poisson…
We derive the phase space density of bosons from a general boson interferometry formula. We find that the phase space density is connected with the two-particles and the single particle density distribution functions. If the boson density…