The Annals of Probability

Optimal Triangulation of Random Samples in the Plane

J. Michael Steele

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Abstract

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.

Article information

Source
Ann. Probab., Volume 10, Number 3 (1982), 548-553.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993766

Digital Object Identifier
doi:10.1214/aop/1176993766

Mathematical Reviews number (MathSciNet)
MR659527

Zentralblatt MATH identifier
0486.60015

JSTOR
links.jstor.org

Subjects
Primary: 60F15: Strong theorems
Secondary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 68C05 68E10

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

Citation

Steele, J. Michael. Optimal Triangulation of Random Samples in the Plane. Ann. Probab. 10 (1982), no. 3, 548--553. doi:10.1214/aop/1176993766. https://projecteuclid.org/euclid.aop/1176993766


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