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.
"Subadditive Euclidean Functionals and Nonlinear Growth in Geometric Probability." Ann. Probab. 9 (3) 365 - 376, June, 1981. https://doi.org/10.1214/aop/1176994411