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

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 p...

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Bibliographic Details
Published inJournal of applied probability Vol. 61; no. 4; pp. 1380 - 1406
Main Authors Dereudre, David, Flimmel, Daniela
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.12.2024
Subjects
Original Article
local energy
60D05
Widom–Rowlinson model
60G55
Voronoi tessellation
density fluctuation
Papangelou intensity
GNZ equation
marked point process
82B21
60K35
nearest-neighbour graph
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Summary: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.
ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2024.21