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Non-hyperuniformity of Gibbs point processes with short-range interactions

Part of: Geometric probability and stochastic geometry Stochastic processes Equilibrium statistical mechanics Special processes

Published online by Cambridge University Press:  02 August 2024

David Dereudre  and
Daniela Flimmel Open the ORCID record for Daniela Flimmel [Opens in a new window]
David Dereudre*
Affiliation:
University of Lille
Daniela Flimmel*
Affiliation:
University of Lille and Charles University
*
*Postal address: University of Lille, CNRS, UMR 8524—Laboratoire Paul Painlevé, F-59000 Lille, France.
*Postal address: University of Lille, CNRS, UMR 8524—Laboratoire Paul Painlevé, F-59000 Lille, France.
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Abstract

We investigate the hyperuniformity of marked Gibbs point processes that have weak dependencies among distant points whilst the interactions of close points are kept arbitrary. Various stability and range assumptions are imposed on the Papangelou intensity in order to prove that the resulting point process is not hyperuniform. The scope of our results covers many frequently used models, including Gibbs point processes with a superstable, lower-regular, integrable pair potential, as well as the Widom–Rowlinson model with random radii and Gibbs point processes with interactions based on Voronoi tessellations and nearest-neighbour graphs.

Keywords

Papangelou intensitymarked point processdensity fluctuationlocal energyGNZ equationVoronoi tessellationnearest-neighbour graphWidom–Rowlinson model

MSC classification

Primary: 60G55: Point processes
Secondary: 60D05: Geometric probability and stochastic geometry 60K35: Interacting random processes; statistical mechanics type models; percolation theory 82B21: Continuum models (systems of particles, etc.)
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 27
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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