Fe b 20 07 Central limit theorem for the on - line nearest - neighbour graph
نویسنده
چکیده
The on-line nearest-neighbour graph on a sequence of 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 a central limit theorem (in the large-sample limit), including an expression for the limiting variance. In contrast, we give a convergence result (with no scaling) for α > d/2. Both these results extend previous work. We also make some progress in the critical case α = d/2.
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