Open Access
2016 Variational principle for Gibbs point processes with finite range interaction
David Dereudre
Electron. Commun. Probab. 21: 1-11 (2016). DOI: 10.1214/16-ECP4368


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.


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David Dereudre. "Variational principle for Gibbs point processes with finite range interaction." Electron. Commun. Probab. 21 1 - 11, 2016.


Received: 16 June 2015; Accepted: 18 January 2016; Published: 2016
First available in Project Euclid: 15 February 2016

zbMATH: 1338.60024
MathSciNet: MR3485379
Digital Object Identifier: 10.1214/16-ECP4368

Primary: 60D05 , 60G10 , 60G55 , 60G57 , 60G60

Keywords: pairwise potential , Quermass-interaction , Specific entropy , Strauss model

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