Electronic Resource
Springer
Probability theory and related fields
92 (1992), S. 247-258
ISSN:
1432-2064
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary Asymptotic results for the Euclidean minimal spanning tree onn random vertices inR d can be obtained from consideration of a limiting infinite forest whose vertices form a Poisson process in allR d. 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 ofR d tends to a constant asn→∞. Whether the limit forest is in fact a single tree is a hard open problem, relating to continuum percolation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01194923
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