Normal and Poisson approximation for Gibbs point processes with pair potentials

Christian Hirsch; Moritz Otto; Anne Marie Svane

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arXiv · 2601.18695

Normal and Poisson approximation for Gibbs point processes with pair potentials

Christian Hirsch·Moritz Otto·Anne Marie Svane

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Abstract

We provide a Poisson approximation result for dependent thinnings of Gibbs point processes as well as qualitative and quantitative central limit theorems for geometric functionals of Gibbs point processes in increasing observation windows. The present paper extends prior work on finite-range Gibbs processes to processes with repulsive pairwise interaction of unbounded interaction range as well as processes on marked Euclidean space. The proofs rely on coupling different Gibbs processes using the disagreement coupling technique, which we generalize to infinite-volume domains under a suitable non-percolation condition. For the case of repulsive pairwise interactions, we introduce a version of disagreement coupling that constructs the Gibbs process by thinning a random connection model thus making previous approximation methods more flexible.

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Christian Hirsch, Moritz Otto, Anne Marie Svane. 2026-01-26. Normal and Poisson approximation for Gibbs point processes with pair potentials. https://arxiv.org/abs/2601.18695

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