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August, 1982 Optimal Triangulation of Random Samples in the Plane
J. Michael Steele
Ann. Probab. 10(3): 548-553 (August, 1982). DOI: 10.1214/aop/1176993766


Let $T_n$ denote the length of the minimal triangulation of $n$ points chosen independently and uniformly from the unit square. It is proved that $T_n/\sqrt n$ converges almost surely to a positive constant. This settles a conjecture of Gyorgy Turan.


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J. Michael Steele. "Optimal Triangulation of Random Samples in the Plane." Ann. Probab. 10 (3) 548 - 553, August, 1982.


Published: August, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0486.60015
MathSciNet: MR659527
Digital Object Identifier: 10.1214/aop/1176993766

Primary: 60F15
Secondary: 60D05 , 68C05 , 68E10

Keywords: Efron-Stein inequality , jackknife , probabilistic algorithm , subadditive Euclidean functionals , Triangulation

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 3 • August, 1982
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