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.
"Continuum percolation for quermass interaction model." Electron. J. Probab. 19 1 - 19, 2014. https://doi.org/10.1214/EJP.v19-2298