Asymptotic theory for the multidimensional random on-line nearest-neighbour graph

Andrew R. Wade

Stochastic Processes and their Applications, 2009, vol. 119, issue 6, 1889-1911

Abstract: The on-line nearest-neighbour graph on a sequence of n uniform random points in (0,1)d () 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 [alpha][set membership, variant](0,d/2], we prove O(max{n1-(2[alpha]/d),logn}) upper bounds on the variance. On the other hand, we give an n-->[infinity] large-sample convergence result for the total power-weighted edge-length when [alpha]>d/2. We prove corresponding results when the underlying point set is a Poisson process of intensity n.

Keywords: Random; spatial; graphs; Network; evolution; Variance; asymptotics; Martingale; differences (search for similar items in EconPapers)
Date: 2009
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