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Erschienen in:
2021 | OriginalPaper | Buchkapitel
Stochastic Point Processes and Random Trees
verfasst von : Prof. Dominique Jeulin
Erschienen in: Morphological Models of Random Structures
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Models of stochastic point processes are basic models of random sets with a rather simple geometry. The archetype model is the Poisson point process, which simulates a population of particles without any spatial interaction. It can be used as seeds for other models developed in other chapters, called grain models. Variants of the Poisson point process use constraints like repulsion, as for the hard-core process. Multi scale models are obtained by means of Cox processes. Iterated Poisson varieties provide models with clusters like alignments on lines or in planes. A short introduction to Gibbs and to Determinantal point processes is given. Finally models of random trees are obtained by branching processes.