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Existence of Gibbsian point processes with geometry-dependent interactions
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  • Published: 25 March 2011

Existence of Gibbsian point processes with geometry-dependent interactions

  • David Dereudre1,
  • Remy Drouilhet2 &
  • Hans-Otto Georgii3 

Probability Theory and Related Fields volume 153, pages 643–670 (2012)Cite this article

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Abstract

We establish the existence of stationary Gibbsian point processes for interactions that act on hyperedges between the points. For example, such interactions can depend on Delaunay edges or triangles, cliques of Voronoi cells or clusters of k-nearest neighbors. The classical case of pair interactions is also included. The basic tools are an entropy bound and stationarity.

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Author information

Authors and Affiliations

  1. Lille Nord de France University, LAMAV UVHC FR 2956, Le Mont Houy, 59313, Valenciennes Cedex 09, France

    David Dereudre

  2. LJK, Université de Grenoble, B.S.H.M., 1251 Av. Centrale, BP 47, 38040, Grenoble Cedex 9, France

    Remy Drouilhet

  3. Mathematisches Institut, Universität München, Theresienstraße 39, 80333, Munich, Germany

    Hans-Otto Georgii

Authors
  1. David Dereudre
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  2. Remy Drouilhet
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  3. Hans-Otto Georgii
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Corresponding author

Correspondence to Hans-Otto Georgii.

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Dereudre, D., Drouilhet, R. & Georgii, HO. Existence of Gibbsian point processes with geometry-dependent interactions. Probab. Theory Relat. Fields 153, 643–670 (2012). https://doi.org/10.1007/s00440-011-0356-5

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  • Received: 15 March 2010

  • Revised: 30 September 2010

  • Published: 25 March 2011

  • Issue Date: August 2012

  • DOI: https://doi.org/10.1007/s00440-011-0356-5

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Keywords

  • Gibbs measure
  • Hypergraph
  • Delaunay mosaic
  • Voronoi tessellation
  • Entropy

Mathematics Subject Classification (2000)

  • Primary 60K35
  • Secondary 60D05
  • 60G55
  • 82B21
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