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November, 1994 Limit Theorems and Rates of Convergence for Euclidean Functionals
C. Redmond, J. E. Yukich
Ann. Appl. Probab. 4(4): 1057-1073 (November, 1994). DOI: 10.1214/aoap/1177004902


A Beardwood-Halton-Hammersley type of limit theorem is established for a broad class of Euclidean functionals which arise in stochastic optimization problems on the $d$-dimensional unit cube. The result, which applies to all functionals having a certain "quasiadditivity" property, involves minimal structural assumptions and holds in the sense of complete convergence. It extends Steele's classic theorem and includes such functionals as the length of the shortest path through a random sample, the minimal length of a tree spanned by a sample, the length of a rectilinear Steiner tree spanned by a sample and the length of a Euclidean matching. A rate of convergence is proved for these functionals.


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C. Redmond. J. E. Yukich. "Limit Theorems and Rates of Convergence for Euclidean Functionals." Ann. Appl. Probab. 4 (4) 1057 - 1073, November, 1994.


Published: November, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0812.60033
MathSciNet: MR1304772
Digital Object Identifier: 10.1214/aoap/1177004902

Primary: 60D05
Secondary: 60C05 , 60F15

Keywords: minimal matching , Minimal spanning tree , rates of convergence , Steiner tree , Subadditive and superadditive functionals , TSP

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.4 • No. 4 • November, 1994
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