Continuum Percolation for Quermass Model

Details Continuum Percolation for Quermass Model Continuum Percolation for Quermass Model

2012-01-11

arxiv.org/abs/1201.2344v1

Mathematics

Probability

21 pages, 2 figures

Scientific paper

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-Poincar\'e 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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