Electronic Journal of Probability

Continuum percolation for quermass interaction model

David Coupier and David Dereudre

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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.

Article information

Electron. J. Probab., Volume 19 (2014), paper no. 35, 19 pp.

Accepted: 19 March 2014
First available in Project Euclid: 4 June 2016

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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]

Stochastic geometry Gibbs point process germ-grain model Quermass interaction percolation phase transition

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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

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