Statistics Papers

Document Type

Journal Article

Date of this Version

1982

Publication Source

The Annals of Probability

Volume

10

Issue

3

Start Page

548

Last Page

553

DOI

10.1214/aop/1176993766

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.

Copyright/Permission Statement

The original and published work is available at: https://projecteuclid.org/euclid.aop/1176993766#abstract

Comments

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.

Keywords

triangulation, probabilistic algorithm, subadditive Euclidean functionals, jackknife, Efron-Stein inequality

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Date Posted: 27 November 2017

This document has been peer reviewed.