Asymptotic theory for the multidimensional random on-line nearest-neighbour graph
نویسنده
چکیده
The on-line nearest-neighbour graph on a sequence of n uniform random points in (0, 1)d (d ∈ N) joins each point after the first to its nearest neighbour amongst its predecessors. For the total power-weighted edge-length of this graph, with weight exponent α ∈ (0, d/2], we prove O(max{n1−(2α/d), log n}) upper bounds on the variance. On the other hand, we give an n → ∞ large-sample convergence result for the total power-weighted edge-length when α > d/2. We prove corresponding results when the underlying point set is a Poisson process of intensity n.
منابع مشابه
Limit theory for the random on-line nearest-neighbor graph
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