Strong laws for Euclidean graphs with general edge weights
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].
Volume (Year): 56 (2002)
Issue (Month): 3 (February)
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- McGivney, K. & Yukich, J. E., 1999. "Asymptotics for Voronoi tessellations on random samples," Stochastic Processes and their Applications, Elsevier, vol. 83(2), pages 273-288, October.
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