Statistics Papers

Document Type

Journal Article

Date of this Version

2016

Publication Source

Annals of Applied Probability

Volume

26

Issue

4

Start Page

2141

Last Page

2168

DOI

10.1214/15-AAP1142

Abstract

We construct a stationary ergodic process X1,X2,…such that each Xt has the uniform distribution on the unit square and the length Ln of the shortest path through the points X1,X2,…,Xn is not asymptotic to a constant times the square root of n. In other words, we show that the Beardwood, Halton, and Hammersley theorem does not extend from the case of independent uniformly distributed random variables to the case of stationary ergodic sequences with uniform marginal distributions.

Copyright/Permission Statement

The original and published work is available at: https://projecteuclid.org/euclid.aoap/1472745454#info

Keywords

traveling salesman problem, Beardwood-Halton-Hammersley theorem, subadditive Euclidean functional, stationary ergodic processes, equidistribution, construction of stationary processes

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Date Posted: 27 November 2017

This document has been peer reviewed.