Continuum Percolation for Quermass Model

David Coupier; David Dereudre

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arXiv · 1201.2344

Continuum Percolation for Quermass Model

David Coupier·David Dereudre

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Abstract

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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David Coupier, David Dereudre. 2012-01-11. Continuum Percolation for Quermass Model. https://arxiv.org/abs/1201.2344

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