Asymptotics for Euclidean minimal spanning trees on random points

@article{Aldous1992AsymptoticsFE,
  title={Asymptotics for Euclidean minimal spanning trees on random points},
  author={D. Aldous and J. Steele},
  journal={Probability Theory and Related Fields},
  year={1992},
  volume={92},
  pages={247-258}
}
SummaryAsymptotic results for the Euclidean minimal spanning tree onn random vertices inRd can be obtained from consideration of a limiting infinite forest whose vertices form a Poisson process in allRd. In particular we prove a conjecture of Robert Bland: the sum of thed'th powers of the edge-lengths of the minimal spanning tree of a random sample ofn points from the uniform distribution in the unit cube ofRd tends to a constant asn→∞.Whether the limit forest is in fact a single tree is a hard… Expand
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