The longest edge of the random minimal spanning tree
Penrose, Mathew D.
Ann. Appl. Probab., Tome 7 (1997) no. 1, p. 340-361 / Harvested from Project Euclid
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For n points placed uniformly at random on the unit square, suppose $M_n$ (respectively, $M'_n$) 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 $n \pi M_n^2 - \log n$ converges weakly to the double exponential; we give a new proof of this. We show that $P[M'_n = M_n] \to 1$, so that the same weak convergence holds for $M'_n$ .
Publié le : 1997-05-14
Classification:  Geometric probability,  minimal spanning tree,  nearest neighbor graph,  extreme values,  Poisson process,  Chen-Stein method,  continuum percolation,  60D05,  60G70,  05C05,  90C27 
@article{1034625335,
     author = {Penrose, Mathew D.},
     title = {The longest edge of the random minimal spanning tree},
     journal = {Ann. Appl. Probab.},
     volume = {7},
     number = {1},
     year = {1997},
     pages = { 340-361},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1034625335}
}

Penrose, Mathew D. The longest edge of the random minimal spanning tree. Ann. Appl. Probab., Tome 7 (1997) no. 1, pp.  340-361. http://gdmltest.u-ga.fr/item/1034625335/