In probability theory, the **Boolean-Poisson model** or simply **Boolean model** for a random subset of the plane (or higher dimensions, analogously) is one of the simplest and most tractable models in stochastic geometry. Take a Poisson point process of rate

To illustrate tractability with one simple formula, the mean density of

As related topics, the case of constant-sized discs is the basic model of continuum percolation and the low-density Boolean models serve as a first-order approximations in the study of extremes in many models.