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Variational principle for Gibbs point processes with finite range interaction. (English) Zbl 1338.60024

Summary: The variational principle for Gibbs point processes with general finite range interaction is proved. Namely, the Gibbs point processes are identified as the minimizers of the free excess energy equals to the sum of the specific entropy and the mean energy. The interaction is very general and includes superstable pairwise potential, finite or infinite multibody potential, geometrical interaction, hardcore interaction. The only restrictive assumption involves the finite range property.

MSC:

60D05 Geometric probability and stochastic geometry
60G10 Stationary stochastic processes
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60G57 Random measures
60G60 Random fields
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