## Electronic Communications in Probability

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

### Variational principle for Gibbs point processes with finite range interaction

#### 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

**Mathematical Reviews number (MathSciNet)**

MR3485379

**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