In a example of Boolean model, points are scattered in the plane according to a homogeneous Poisson process of intensity $λ$. On each of these points a disc of fixed radius $r$ is placed.

Similar to the question posted before: Any expression for the probability of a hard sphere in Boolean model

My question is: What is the probability if a new disc of radius rh is placed without increase of the area of discs in this Boolean model? That means the new disc is fully overlapped by the existing discs.


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