Date of this Version
Annals of Applied Probability
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.
The original and published work is available at: https://projecteuclid.org/euclid.aoap/1472745454#info
traveling salesman problem, Beardwood-Halton-Hammersley theorem, subadditive Euclidean functional, stationary ergodic processes, equidistribution, construction of stationary processes
Arlotto, A., & Steele, J. (2016). Beardwood-Halton-Hammersly Theorem for Stationary Ergodic Sequences: A Counterexample. Annals of Applied Probability, 26 (4), 2141-2168. http://dx.doi.org/10.1214/15-AAP1142
Date Posted: 27 November 2017
This document has been peer reviewed.