✦ LIBER ✦

On the variance of the random sphere of influence graph

✍ Scribed by P. Hitczenko; S. Janson; J. E. Yukich

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 219 KB
Volume: 14
Category: Article
ISSN: 1042-9832
DOI: 10.1002/(sici)1098-2418(199903)14:2<139::aid-rsa2>3.0.co;2-e

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✦ Synopsis

We show that the variance of the number of edges in the random sphere of influence graph built on n i.i.d. sites which are uniformly distributed over the unit cube in R d , grows linearly with n. This is then used to establish a central limit theorem for the number of edges in the random sphere of influence graph built on a Poisson number of sites. Some related proximity graphs are discussed as well.

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