The longest edge of the random minimal spanning tree

For n points placed uniformly at random on the unit square, suppose Mn (respectively,Mn) denotes the longest edge-length of the nearest neighbor graph (respectively, the minimal spanning tree) on these points. It is known that the distribution of nπMn−log n converges weakly to the double exponential; we give a new proof of this. We show that P’Mn =Mn“ → 1, so that the same weak convergence holds for Mn.

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