Hi, there. I am finding the distribution of intersecting area of multiple discs. Let's say there is a disk (mother plane for Poisson points deployment) with radius $A$. In this disk, a number of points which are the centers of disks having radii $B(>A)$ are deployed uniformly. Here, the number of deployed disk is assumed to follow the Poisson dist. Then, I wonder if there is any closed form or way to characterize each intersecting areas. For example, if there are two points in the mother plane, then there are three($2^2-1$) segments and each segment has their area, which are the functions of distance between two center points of discs. As the number of points deployed increases to $N$, then the number of segments increases to ($2^N-1$). They are the function of distances of each points. Does anyone have the clue for addressing this problem?
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