Electronic Communications in Probability

Variational principle for Gibbs point processes with finite range interaction

David Dereudre

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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.

Article information

Electron. Commun. Probab., Volume 21 (2016), paper no. 10, 11 pp.

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

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Zentralblatt MATH identifier

Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60G10: Stationary processes 60G55: Point processes 60G57: Random measures 60G60: Random fields

specific entropy pairwise potential Strauss model Quermass-interaction

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Dereudre, David. Variational principle for Gibbs point processes with finite range interaction. Electron. Commun. Probab. 21 (2016), paper no. 10, 11 pp. doi:10.1214/16-ECP4368. https://projecteuclid.org/euclid.ecp/1455560034

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