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

DOI10.1016/j.spa.2008.09.006zbMath1163.60005arXivmath/0702414OpenAlexW2077586119MaRDI QIDQ1019614

Andrew R. Wade

Publication date: 4 June 2009

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702414

zbMATH Keywords

martingale differencesnetwork evolutionvariance asymptoticsrandom spatial graphs

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Random graphs (graph-theoretic aspects) (05C80) Stochastic network models in operations research (90B15) (L^p)-limit theorems (60F25)

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Cites Work

• On central limit theorems in geometrical probability
• A general limit theorem for recursive algorithms and combinatorial structures
• Gaussian limits for random measures in geometric probability
• The central limit theorem for weighted minimal spanning trees on random points
• Weak laws of large numbers in geometric probability
• Central limit theorems for some graphs in computational geometry.
• The diameter of a scale-free random graph
• Gaussian limits for random geometric measures
• Multivariate spatial central limit theorems with applications to percolation and spatial graphs
• Explicit laws of large numbers for random nearest-neighbour-type graphs
• Probability with Martingales
• The Structure and Function of Complex Networks
• Random Geometric Graphs
• Limit theory for the random on‐line nearest‐neighbor graph
• On the total length of the random minimal directed spanning tree
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