Asymptotics of power-weighted Euclidean functionals

Sungchul Lee

doi:10.1016/S0304-4149(98)00065-9

Asymptotics of power-weighted Euclidean functionals

Sungchul Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Let {X_i:i≥1} be i.i.d. points in R^d, d≥2, and let L_MM({X₁,...,X_n},p), L_MST({X₁,...,X_n},p), L_TSP({X₁,...,X_n},p), be the length of the minimal matching, the minimal spanning tree, the traveling salesman problem, respectively, on {X₁,...,X_n} with weight function w(e)=e^p. If the common distribution satisfies certain regularity conditions, then the strong law of large numbers for the above three Euclidean functionals, 1≤p<d, has been obtained. In this paper we show that the same type of result holds for 0<p<1.

Original language	English
Pages (from-to)	109-116
Number of pages	8
Journal	Stochastic Processes and their Applications
Volume	79
Issue number	1
DOIs	https://doi.org/10.1016/S0304-4149(98)00065-9
Publication status	Published - 1999 Jan 1

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modelling and Simulation
Applied Mathematics

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abstract = "Let {Xi:i≥1} be i.i.d. points in Rd, d≥2, and let LMM({X1,...,Xn},p), LMST({X1,...,Xn},p), LTSP({X1,...,Xn},p), be the length of the minimal matching, the minimal spanning tree, the traveling salesman problem, respectively, on {X1,...,Xn} with weight function w(e)=ep. If the common distribution satisfies certain regularity conditions, then the strong law of large numbers for the above three Euclidean functionals, 1≤p",

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AB - Let {Xi:i≥1} be i.i.d. points in Rd, d≥2, and let LMM({X1,...,Xn},p), LMST({X1,...,Xn},p), LTSP({X1,...,Xn},p), be the length of the minimal matching, the minimal spanning tree, the traveling salesman problem, respectively, on {X1,...,Xn} with weight function w(e)=ep. If the common distribution satisfies certain regularity conditions, then the strong law of large numbers for the above three Euclidean functionals, 1≤p

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JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 1

ER -

Asymptotics of power-weighted Euclidean functionals

Abstract

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