Date of this Version
The Annals of Probability
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.
The original and published work is available at: https://projecteuclid.org/euclid.aop/1176993766#abstract
triangulation, probabilistic algorithm, subadditive Euclidean functionals, jackknife, Efron-Stein inequality
Steele, J. M. (1982). Optimal Triangulation of Random Samples in the Plane. The Annals of Probability, 10 (3), 548-553. http://dx.doi.org/10.1214/aop/1176993766
Date Posted: 27 November 2017
This document has been peer reviewed.