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Limit theory for the random on-line nearest-neighbour graph

Penrose, M.D. and Wade, A.R. (2008) Limit theory for the random on-line nearest-neighbour graph. Random Structures and Algorithms, 32 (2). pp. 125-156. ISSN 1042-9832

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Abstract

In the on-line nearest-neighbour graph (ONG), each point after the first in a sequence of points in Rd is joined by an edge to its nearest neighbour amongst those points that precede it in the sequence. We study the large-sample asymptotic behaviour of the total power-weighted length of the ONG on uniform random points in (0, 1)d. In particular, for d = 1 and weight exponent > 1/2, the limiting distribution of the centred total weight is characterized by a distributional fixed point equation. As an ancillary result, we give exact expressions for the expectation and variance of the standard nearest-neighbour (directed) graph on uniform random points in the unit interval.

Item type: Article
ID code: 13396
Keywords: nearest-neighbour graph, spatial network evolution, weak convergence, fixed-point equation, divide-and-conquer, Probabilities. Mathematical statistics, Mathematics, Computer Graphics and Computer-Aided Design, Software, Applied Mathematics, Mathematics(all)
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Depositing user: Mrs Carolynne Westwood
Date Deposited: 12 Nov 2009 14:14
Last modified: 18 Jun 2015 04:34
URI: http://strathprints.strath.ac.uk/id/eprint/13396

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