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24 votes
3 answers
4k views

What upper bounds are known for the diameter of the minimum spanning tree of $n$ uniformly random points in $[0,1]^2$?

Let $P$ be a pointset consisting of $n$ uniformly random elements of $[0,1]^2$. It is known that the diameter (greatest number of edges in any shortest path between two points) of the Delaunay ...
2 votes
1 answer
305 views

Distribution of area of randomly placed circles

I've searched the web now for ages to try and find a paper on the asymptotic distribution of the area of the union of randomly placed discs on the plane. Ideally, I would be looking for the discs to ...