Wade, Andrew (2007) Explicit laws of large numbers for random nearest-neighbour-type graphs. Advances in Applied Probability, 39 (2). pp. 326-342. ISSN 0001-8678Full text not available in this repository. (Request a copy from the Strathclyde author)
Under the unifying umbrella of a general result of Penrose & Yukich [Ann. Appl. Probab., (2003) 13, 277--303] we give laws of large numbers (in the Lp sense) for the total power-weighted length of several nearest-neighbour 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 k-nearest neighbours graph, the Gabriel graph, the minimal directed spanning forest, and the on-line nearest-neighbour graph.
|Keywords:||nearest-neighbour-type 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 2017 03:25|