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Germ-grain Model

Definition

In continuum percolation theory, the so-called germ-grain model is an obvious generalization of both the Boolean and Boolean-Poisson models which is driven by an arbitrary stationary point process X and which assigns to the points x_i element X arbitrary compact sets A_i in R^d rather than the standard closed balls. In this scenario, the points x_i are known as the germs while the sets A_i are known as grains. It is not uncommon to consider the union of all grains in a germ-grain model, a collection which is sometimes referred to as the grain cover. The grain cover is sometimes referred to as the basis of the model in question.

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