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Open Access Publications from the University of California

Asymptotics for Euclidean minimal spanning trees on random points

  • Author(s): Aldous, D
  • Steele, JM
  • et al.

Asymptotic results for the Euclidean minimal spanning tree on n random vertices in Rd can be obtained from consideration of a limiting infinite forest whose vertices form a Poisson process in all Rd. In particular we prove a conjecture of Robert Bland: the sum of the d'th powers of the edge-lengths of the minimal spanning tree of a random sample of n points from the uniform distribution in the unit cube of Rd tends to a constant as n→∞. Whether the limit forest is in fact a single tree is a hard open problem, relating to continuum percolation. © 1992 Springer-Verlag.

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