Gibbsian representation for point processes via hyperedge potentials
- Jahnel, Benedikt
- 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 . These potentials are natural generalizations of physical multibody potentials which are useful in models of stochastic geometry.