A limit theorem is established for a class of random processes (called here subadditive Euclidean functionals) which arise in problems of geometric probability. Particular examples include the length of shortest path through a random sample, the length of a rectilinear Steiner tree spanned by a sample, and the length of a minimal matching. Also, a uniform convergence theorem is proved which is needed in Karp's probabilistic algorithm for the traveling salesman problem.
@article{1176994411,
author = {Steele, J. Michael},
title = {Subadditive Euclidean Functionals and Nonlinear Growth in Geometric Probability},
journal = {Ann. Probab.},
volume = {9},
number = {6},
year = {1981},
pages = { 365-376},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994411}
}
Steele, J. Michael. Subadditive Euclidean Functionals and Nonlinear Growth in Geometric Probability. Ann. Probab., Tome 9 (1981) no. 6, pp. 365-376. http://gdmltest.u-ga.fr/item/1176994411/