A critical constant for the k nearest-neighbour model
نویسندگان
چکیده
منابع مشابه
A Critical Constant for the k Nearest-Neighbour Model
Let P be a Poisson process of intensity one in a square Sn of area n. For a fixed integer k, join every point of P to its k nearest neighbours, creating an undirected random geometric graph Gn,k. We prove that there exists a critical constant ccrit such that for c < ccrit, Gn,⌊c logn⌋ is disconnected with probability tending to 1 as n → ∞, and for c > ccrit, Gn,⌊c logn⌋ is connected with probab...
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ژورنال
عنوان ژورنال: Advances in Applied Probability
سال: 2009
ISSN: 0001-8678,1475-6064
DOI: 10.1017/s0001867800003116