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Subadditive Euclidean Functionals and Nonlinear Growth in Geometric Probability

J. Michael Steele
The Annals of Probability
Vol. 9, No. 3 (Jun., 1981), pp. 365-376
Stable URL: http://www.jstor.org/stable/2243524
Page Count: 12
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Subadditive Euclidean Functionals and Nonlinear Growth in Geometric Probability
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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.

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