Continuum percolation for quermass model

David Coupier (Université Lille 1)
David Dereudre (Université Lille 1)


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.

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Pages: 1-19

Publication Date: March 19, 2014

DOI: 10.1214/EJP.v19-2298


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