Electronic Journal of Probability
- Electron. J. Probab.
- Volume 19 (2014), paper no. 35, 19 pp.
Continuum percolation for quermass interaction model
The continuum percolation for Markov (or Gibbs) germ-grain models in dimension 2 is investigated. The grains are assumed circular with random radii on a compact support. The morphological interaction is the so-called quermass interaction defined by a linear combination of the classical Minkowski functionals (area, perimeter and Euler-Poincaré characteristic). We show that the percolation occurs for any coefficient of this linear combination and for a large enough activity parameter. An application to the phase transition of the multi-type quermass model is given.
Electron. J. Probab., Volume 19 (2014), paper no. 35, 19 pp.
Accepted: 19 March 2014
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B05: Classical equilibrium statistical mechanics (general) 82B21: Continuum models (systems of particles, etc.) 82B26: Phase transitions (general) 82B43: Percolation [See also 60K35]
This work is licensed under a Creative Commons Attribution 3.0 License.
Coupier, David; Dereudre, David. Continuum percolation for quermass interaction model. Electron. J. Probab. 19 (2014), paper no. 35, 19 pp. doi:10.1214/EJP.v19-2298. https://projecteuclid.org/euclid.ejp/1465065677