Optimal Triangulation of Random Samples in the Plane
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triangulation
probabilistic algorithm
subadditive Euclidean functionals
jackknife
Efron-Stein inequality
Physical Sciences and Mathematics
probabilistic algorithm
subadditive Euclidean functionals
jackknife
Efron-Stein inequality
Physical Sciences and Mathematics
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Abstract
Let Tn denote the length of the minimal triangulation of n points chosen independently and uniformly from the unit square. It is proved that Tn/√n converges almost surely to a positive constant. This settles a conjecture of György Turán.
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1982
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The Annals of Probability
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At the time of publication, author J. Michael Steele was affiliated with Stanford University. Currently, he is a faculty member at the Statistics Department at the University of Pennsylvania.