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This work improves the existing central limit theorems (CLTs) for geometric functionals of Gibbs processes in three aspects. First, we derive a CLT for weakly stabilizing functionals, thereby improving on the previously used assumption of…

Probability · Mathematics 2024-06-12 Christian Hirsch , Moritz Otto , Anne Marie Svane

We discuss a thinning and an embedding procedure to construct finite Gibbs processes with a given Papangelou intensity. Extending the approach in Hofer-Temmel (2019) and Hofer-Temmel and Houdebert (2019) we will use this to couple two…

Probability · Mathematics 2023-01-24 Günter Last , Moritz Otto

We generalise disagreement percolation to Gibbs point processes of balls with varying radii. This allows to establish the uniqueness of the Gibbs measure and exponential decay of pair correlations in the low activity regime by comparison…

Probability · Mathematics 2019-04-24 Christoph Hofer-Temmel , Pierre Houdebert

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…

Probability · Mathematics 2024-02-14 Moritz Otto

The intensity of a Gibbs point process is usually an intractable function of the model parameters. For repulsive pairwise interaction point processes, this intensity can be expressed as the Laplace transform of some particular function.…

Methodology · Statistics 2017-12-11 Jean-François Coeurjolly , Frédéric Lavancier

This paper is concerned with statistical inference for infinite range interaction Gibbs point processes and in particular for the large class of Ruelle superstable and lower regular pairwise interaction models. We extend classical…

Statistics Theory · Mathematics 2015-10-05 Jean-François Coeurjolly , Frédéric Lavancier

The class of Gibbs point processes (GPP) is a large class of spatial point processes able to model both clustered and repulsive point patterns. They are specified by their conditional intensity, which for a point pattern $\mathbf{x}$ and a…

Statistics Theory · Mathematics 2023-01-09 Ismaïla Ba , Jean-François Coeurjolly , Francisco Cuevas-Pacheco

We investigate the hyperuniformity of marked Gibbs point processes with weak dependencies among distant points whilst the interactions of close points are kept arbitrary. Some variants of stability and range assumptions are posed on the…

Probability · Mathematics 2024-01-17 David Dereudre , Daniela Flimmel

We study a stationary Gibbs particle process with deterministically bounded particles on Euclidean space defined in terms of an activity parameter and non-negative interaction potentials of finite range. Using disagreement percolation we…

Probability · Mathematics 2020-09-08 Viktor Beneš , Christoph Hofer-Temmel , Günter Last , Jakub Večeřa

The Gibbs point processes (GPP) constitute a large class of point processes with interaction between the points. The interaction can be attractive, repulsive, depending on geometrical features whereas the null interaction is associated to…

Probability · Mathematics 2018-04-09 David Dereudre

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…

Probability · Mathematics 2013-04-18 Kaspar Stucki , Dominic Schuhmacher

We study computational aspects of repulsive Gibbs point processes, which are probabilistic models of interacting particles in a finite-volume region of space. We introduce an approach for reducing a Gibbs point process to the hard-core…

Data Structures and Algorithms · Computer Science 2023-12-15 Tobias Friedrich , Andreas Göbel , Maximilian Katzmann , Martin Krejca , Marcus Pappik

We consider the Gibbs measure of a general interacting particle system for a certain class of ``weakly interacting" kernels. In particular, we show that the local point process converges to a Poisson point process as long as the inverse…

Probability · Mathematics 2025-06-18 David Padilla-Garza , Luke Peilen , Eric Thoma

We construct marked Gibbs point processes in $\mathbb{R}^d$ under quite general assumptions. Firstly, we allow for interaction functionals that may be unbounded and whose range is not assumed to be uniformly bounded. Indeed, our typical…

Probability · Mathematics 2022-07-15 Sylvie Roelly , Alexander Zass

In this paper, we present a large-deviation theory developed for functionals of canonical Gibbs processes, i.e., Gibbs processes with respect to the binomial point process. We study the regime of a fixed intensity in a sequence of…

Probability · Mathematics 2025-05-29 Christian Hirsch , Martina Petráková

The variational principle for Gibbs point processes with general finite range interaction is proved. Namely, the Gibbs point processes are identified as the minimizers of the free excess energy equals to the sum of the specific entropy and…

Probability · Mathematics 2015-06-17 David Dereudre

We present new Poisson process approximation results for stabilizing functionals of Poisson and binomial point processes. These functionals are allowed to have an unbounded range of interaction and encompass many examples in stochastic…

Probability · Mathematics 2021-04-28 Omer Bobrowski , Matthias Schulte , D. Yogeshwaran

A new type of dependent thinning for point processes in continuous space is proposed, which leverages the advantages of determinantal point processes defined on finite spaces and, as such, is particularly amenable to statistical, numerical,…

Machine Learning · Computer Science 2019-06-19 Bartłomiej Błaszczyszyn , Paul Keeler

We present a perfect sampling algorithm for Gibbs point processes, based on the partial rejection sampling of Guo et al. (2017). Our particular focus is on pairwise interaction processes, penetrable spheres mixture models and…

Probability · Mathematics 2019-01-18 Sarat B. Moka , Dirk P. Kroese

Disagreement percolation connects a Gibbs lattice gas and i.i.d. site percolation on the same lattice such that non-percolation implies uniqueness of the Gibbs measure. This work generalises disagreement percolation to the hard-sphere model…

Probability · Mathematics 2019-07-02 Christoph Hofer-Temmel
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