Strong laws for Euclidean graphs with general edge weights

Raul Jimenez () and J. E. Yukich

Statistics & Probability Letters, 2002, vol. 56, issue 3, 251-259

Abstract: Consider a random Euclidean graph G with a vertex set consisting of i.i.d. random variables with a common density f. Let the edge lengths e, e[set membership, variant]G, be weighted by a function [phi]. We provide sufficient conditions on G and [phi] guaranteeing that the total edge length functional [summation operator]e[set membership, variant]G [phi](e) satisfies a strong law of large numbers. The limiting constant is shown to depend explicitly on f and [phi].

Keywords: Laws; of; large; numbers; Random; graphs; Nearest; neighbors; graph; Voronoi; and; Delaunay; graphs (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (1)

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