Electronic Communications in Probability

Variational principle for Gibbs point processes with finite range interaction

David Dereudre

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1455560034

Digital Object Identifier
doi:10.1214/16-ECP4368

Zentralblatt MATH identifier
1338.60024

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

Keywords
specific entropy pairwise potential Strauss model Quermass-interaction

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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