Continuum percolation for quermass model. (English) Zbl 1291.60201

Coupier, David; Dereudre, David

Electron. J. Probab. 19, Paper No. 35, 19 p. (2014).

Summary: The continuum percolation for Markov (or Gibbs) germ-grain models 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.

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
82B05	Classical equilibrium statistical mechanics (general)
82B21	Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics
82B26	Phase transitions (general) in equilibrium statistical mechanics
82B43	Percolation

Keywords:

stochastic geometry; Gibbs point process; germ-grain model; quermass interaction; percolation; phase transition