In most modern literature, a Boolean model is a probabilistic model of continuum percolation theory characterized by the existence of a stationary point process X and a random variable ρ which independently determine the centers and the random radii of a collection of closed balls in R^d for some d. In this case, the model is said to be driven by X. Worth noting is that the most intuitive ideas about constructing a feasible model using X and ρ often lead to unexpected and undesirable results. For that reason, some more sophisticated machinery and quite a bit of care is needed to translate from the language of X and ρ into a reasonable model of continuum percolation. The formal construction is as follows.

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