Nearest-neighbor graphs on the Cantor set
Nathan Shank
Source: Adv. in Appl. Probab. Volume 41, Number 1 (2009), 038-062.
Abstract
Let 𝛘n be a collection of n uniform, independent, and identically distributed points on the Cantor ternary set. We consider the asymptotics for the expected total edge length of the directed and undirected nearest-neighbor graph on 𝛘n. We prove convergence to a constant of the rescaled expected total edge length of this random graph. The rescaling factor is a function of the fractal dimension and has a log-periodic, nonconstant behavior.
Primary Subjects: 60F05
Secondary Subjects: 60D05
Keywords: Nearest neighbor; Cantor set; law of large numbers
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aap/1240319576
Digital Object Identifier: doi:10.1239/aap/1240319576
Zentralblatt MATH identifier:
1161.60009
Mathematical Reviews number (MathSciNet):
MR2514945
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Advances in Applied Probability
