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Boolean cluster models: mean cluster dilations and spherical contact distances. (English) Zbl 0892.60015
Summary: Various Boolean cluster fields in $$\mathbb R^d$$ with clusters ranging from deterministic arrangements (vertices of simplices and cubes) and random $$N$$-tuples of points in a ball to mixtures of clusters random in arrangement and number of points are introduced and examined. The formulae for the mean spherical dilation of clusters are derived and discussed in terms of their expected volumes, then they are used to compute the distribution function of the (first) spherical contact. The general results are illustrated by several numerical examples showing the behaviour of models depending on the cluster parameters and on the dimension of the embedding space.
##### MSC:
 60D05 Geometric probability and stochastic geometry 60G55 Point processes (e.g., Poisson, Cox, Hawkes processes) 62M30 Inference from spatial processes
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