Explicit laws of large numbers for random nearestneighbourtype graphs
Wade, Andrew (2007) Explicit laws of large numbers for random nearestneighbourtype graphs. Advances in Applied Probability, 39 (2). pp. 326342. ISSN 00018678
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Under the unifying umbrella of a general result of Penrose & Yukich [Ann. Appl. Probab., (2003) 13, 277303] we give laws of large numbers (in the Lp sense) for the total powerweighted length of several nearestneighbour type graphs on random point sets in Rd, d in N. Some of these results are known; some are new. We give limiting constants explicitly, where previously they have been evaluated in less generality or not at all. The graphs we consider include the knearest neighbours graph, the Gabriel graph, the minimal directed spanning forest, and the online nearestneighbour graph.


Item type: Article ID code: 34458 Dates: DateEventJune 2007PublishedKeywords: nearestneighbourtype graph, law of large numbers, spanning forest, spatial network evolution, explicit laws, large numbers, random, Probabilities. Mathematical statistics, Applied Mathematics, Statistics and Probability Subjects: Science > Mathematics > Probabilities. Mathematical statistics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 04 Nov 2011 12:51 Last modified: 20 Jan 2021 19:40 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/34458