The Annals of Probability

Subadditive Euclidean Functionals and Nonlinear Growth in Geometric Probability

J. Michael Steele

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Abstract

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 information

Source
Ann. Probab. Volume 9, Number 3 (1981), 365-376.

Dates
First available: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176994411

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aop/1176994411

Mathematical Reviews number (MathSciNet)
MR626571

Zentralblatt MATH identifier
0461.60029

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 60F15: Strong theorems 60C05: Combinatorial probability 60G55: Point processes

Keywords
Subadditive process traveling salesman problem Steiner tree Euclidean functional

Citation

Steele, J. Michael. Subadditive Euclidean Functionals and Nonlinear Growth in Geometric Probability. The Annals of Probability 9 (1981), no. 3, 365--376. doi:10.1214/aop/1176994411. http://projecteuclid.org/euclid.aop/1176994411.


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