WIAS Preprint No. 2414, (2017)

Gibbsian representation for point processes via hyperedge potentials


  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Külske, Christof

2010 Mathematics Subject Classification

  • 82B21 60K35


  • Gibbsian point processes, Koslov theorem, Sullivan theorem, hyperedge potentials, Widom-Rowlinson model




We consider marked point processes on the d-dimensional euclidean space, defined in terms of a quasilocal specification based on marked Poisson point processes. We investigate the possibility of constructing uniformly absolutely convergent Hamiltonians in terms of hyperedge potentials in the sense of Georgii [2]. These potentials are natural generalizations of physical multibody potentials which are useful in models of stochastic geometry.

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